{"id":7664,"date":"2013-08-20T02:57:57","date_gmt":"2013-08-20T02:57:57","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=7664"},"modified":"2026-03-26T09:29:45","modified_gmt":"2026-03-26T14:29:45","slug":"converse-inverse-and-contrapositive","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/converse-inverse-and-contrapositive\/","title":{"rendered":"Converse, Inverse, and Contrapositive"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_j7VXw-FsnnQ\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_j7VXw-FsnnQ\" data-source-videoID=\"j7VXw-FsnnQ\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Converse, Inverse, and Contrapositive Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Converse, Inverse, and Contrapositive\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_j7VXw-FsnnQ:hover {cursor:pointer;} img#videoThumbnailImage_j7VXw-FsnnQ {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1202-Converse-Inverse-and-Contrapositive-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_j7VXw-FsnnQ\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_j7VXw-FsnnQ\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Converse, Inverse, and Contrapositive\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_j7VXw-FsnnQ\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_j7VXw-FsnnQ\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_j7VXw-FsnnQ\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction jNB_Function() {\n  var x = document.getElementById(\"jNB\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"jNB_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"jNB\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Basic_Statements\" class=\"smooth-scroll\">Basic Statements<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Conditional_Statements\" class=\"smooth-scroll\">Conditional Statements<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Converse,_Inverse,_and_Contrapositive_Statement_Examples\" class=\"smooth-scroll\">Converse, Inverse, and Contrapositive Statement Examples<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Review\" class=\"smooth-scroll\">Review<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Converse,_Inverse,_and_Contrapositive_Practice_Questions\" class=\"smooth-scroll\">Converse, Inverse, and Contrapositive Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on mathematical statements! Today, we\u2019ll be exploring the logic that appears in the language of math. Specifically, we will learn how to interpret a math statement to create what are known as converse, inverse, and contrapositive statements. These, along with some reasoning skills, allow us to make sense of problems presented in math. Let\u2019s get started!<\/p>\n<h2><span id=\"Basic_Statements\" class=\"m-toc-anchor\"><\/span>Basic Statements<\/h2>\n<p>\nLet\u2019s first take a look at a <strong>basic statement<\/strong>, which can be either true or false, but never both. For example, a declarative statement pronounces a fact, like \u201cthe Sun is hot.\u201d We know this is a statement because the Sun cannot be both hot and not hot at the same time. This declarative statement could also be referred to as a <strong>proposition<\/strong>.<\/p>\n<h2><span id=\"Conditional_Statements\" class=\"m-toc-anchor\"><\/span>Conditional Statements<\/h2>\n<p>\nTwo independent statements can be related to each other in a logic structure called a <strong>conditional statement<\/strong>. The first statement is presented with \u201cif,\u201d and is referred to as the <strong>hypothesis<\/strong>. The second statement is linked with \u201cthen\u201d, and is known as the <strong>conclusion<\/strong>. The notation associated with conditional statements typically uses the variable \\(p\\) for the hypothesis statement, and \\(q\\) for the conclusion. <\/p>\n<div class=\"examplesentence\">\\(p\\rightarrow q\\)<\/div>\n<p>\n&nbsp;<br \/>\nIn words, this would be read as, \u201cIf \\(p\\), then \\(q\\).\u201d <\/p>\n<p>When the hypothesis and conclusion are identified in a statement, three other statements can be derived:<\/p>\n<ol>\n<li style=\"margin-bottom: 12px;\">The <strong>converse statement<\/strong> is notated as \\(q\\rightarrow p\\) (if \\(q\\), then \\(p\\)). The original statements switch positions in the original \u201cif-then\u201d statement.\n<li style=\"margin-bottom: 12px;\">The <strong>inverse statement<\/strong> assumes the opposite of each of the original statements and is notated \\(\\sim p\\rightarrow \\sim q\\) (if not \\(p\\), then not \\(q\\)).\n<li>The <strong>contrapositive statement<\/strong> is a combination of the previous two. The positions of \\(p\\) and \\(q\\) of the original statement are switched, and then the opposite of each is considered: \\(\\sim q \\rightarrow \\sim p\\) (if not \\(q\\), then not \\(p\\)).<\/li>\n<\/ol>\n<h2><span id=\"Converse,_Inverse,_and_Contrapositive_Statement_Examples\" class=\"m-toc-anchor\"><\/span>Converse, Inverse, and Contrapositive Statement Examples<\/h2>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nAn example will help to make sense of this new terminology and notation. Let\u2019s start with a conditional statement and turn it into our three other statements.<\/p>\n<div class=\"transcriptcallout\"><strong>Conditional statement<\/strong>: \u201cIf it is raining, then the grass is wet.\u201d<\/div>\n<p>\n&nbsp;<br \/>\nThe first step is to identify the hypothesis and conclusion statements. Conditional statements make this pretty easy, as the hypothesis follows <em>if<\/em> and the conclusion follows <em>then<\/em>. The hypothesis is <em>it is raining<\/em> and the conclusion is <em>grass is wet<\/em>.<\/p>\n<div class=\"transcriptcallout\"><strong>Hypothesis<\/strong>, \\(p\\): <em>it is raining<\/em><br \/>\n<strong>Conclusion<\/strong>, \\(q\\): <em>grass is wet<\/em><\/div>\n<p>\n&nbsp;<br \/>\nNow we can use the definitions that we introduced earlier to create the three other statements.<\/p>\n<ul>\n<li>Our <strong>converse statement<\/strong> would be: \u201cIf the grass is wet, then it is raining.\u201d\n<li>Our <strong>inverse statement<\/strong> would be: \u201cIf it is NOT raining, then the grass is NOT wet.\u201d\n<li>Our <strong>contrapositive statement<\/strong> would be: \u201cIf the grass is NOT wet, then it is NOT raining.\u201d<\/li>\n<\/ul>\n<h3><span id=\"Logically_Equivalent_Statements\" class=\"m-toc-anchor\"><\/span>Logically Equivalent Statements<\/h3>\n<p>\nYou may be wondering why we would want to go through the trouble of rearranging and considering the \u201copposite\u201d of the hypothesis and conclusion statements. How is this helpful? The key is in the relationship between the statements. If we know that a statement is true (or false), then we can assume that another is also true (or false). The statements that are related in this way are considered <strong>logically equivalent<\/strong>.<\/p>\n<p>For example, consider the statement, \u201cIf it is raining, then the grass is wet\u201d to be TRUE. Then you can assume that the contrapositive statement, \u201cIf the grass is NOT wet, then it is NOT raining\u201d is also TRUE.<\/p>\n<p>Likewise, the converse statement, \u201cIf the grass is wet, then it is raining\u201d is logically equivalent to the inverse statement, \u201cIf it is NOT raining, then the grass is NOT wet.\u201d<\/p>\n<p>These relationships are particularly helpful in math courses when you are asked to prove theorems based on definitions that are already known. Much of that work is beyond the scope of this video, but the following examples will help to illustrate the relationships of logically equivalent statements.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nHere is a typical example of a TRUE statement that would be made in a geometry class based on the definition of <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/congruent-angles\/\">congruent angles<\/a>:<\/p>\n<div class=\"transcriptcallout\">Two angles with equal measure are congruent.<\/div>\n<p>\n&nbsp;<br \/>\nAs you can see, this is not a conditional statement, but we can rewrite it in the \u201cif-then\u201d structure to identify the hypothesis and conclusion statements as follows:<\/p>\n<div class=\"transcriptcallout\"><em>If<\/em> two angles have the same measure, <em>then<\/em> the two angles are congruent.<\/div>\n<p>\n&nbsp;<br \/>\nNow we have a hypothesis and a conclusion.<\/p>\n<div class=\"transcriptcallout\"><strong>Hypothesis<\/strong>: \u201cTwo angles have the same measure\u201d<br \/>\n<strong>Conclusion<\/strong>: \u201cTwo angles are congruent\u201d<\/div>\n<p>\n&nbsp;<br \/>\nBecause the conditional statement and the contrapositive are logically equivalent, we can assume the following to be TRUE:<\/p>\n<div class=\"transcriptcallout\">If the two angles are NOT congruent, then the two angles do NOT have the&nbsp;same&nbsp;measure.<\/div>\n<p>\n&nbsp;<br \/>\nIt follows that the converse statement, \u201cIf two angles are congruent, then the two angles have the same measure,\u201d is logically equivalent to the inverse statement, \u201cIf two angles do NOT have the same measure, then they are NOT congruent.\u201d<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nHere is another example of a TRUE statement:<\/p>\n<div class=\"transcriptcallout\">A square is a rectangle.<\/div>\n<p>\n&nbsp;<br \/>\nThe conditional statement would be \u201cIf a figure is a square, then it is a rectangle,\u201d which gives us our hypothesis and conclusion.<\/p>\n<div class=\"transcriptcallout\"><strong>Hypothesis<\/strong>: a figure is a square<br \/>\n<strong>Conclusion<\/strong>: the figure is a rectangle<\/div>\n<p>\n&nbsp;<br \/>\nBecause the contrapositive statement is logically equivalent, we can assume that \u201cIf the figure is NOT a rectangle, then the figure is NOT a square\u201d is also a TRUE statement.<\/p>\n<p>However, the converse statement can be disproved.<\/p>\n<div class=\"transcriptcallout\"><strong>Converse<\/strong>: &#8220;If the figure is a rectangle, then it is a square.\u201d<\/div>\n<p>\n&nbsp;<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/polygon-screeenshoot-300x168.png\" alt=\"\" width=\"600\" height=\"336\" class=\"aligncenter size-medium wp-image-84880\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/polygon-screeenshoot-300x168.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/polygon-screeenshoot.png 723w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>As can be seen in the diagram above, squares are a type of rectangle and a rectangle is a type of <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/polygons\/\">polygon<\/a>. However, a square is a special type of rectangle that has four sides of equal length. Not all rectangles have four equal sides like a square, so our converse statement is FALSE.<\/p>\n<p>Accordingly, the inverse statement is also FALSE because they are logically equivalent:<\/p>\n<div class=\"transcriptcallout\">If the figure is NOT a square, then it is NOT a rectangle.<\/div>\n<p>\n&nbsp;<br \/>\nIn summary, the original statement is logically equivalent to the contrapositive, and the converse statement is logically equivalent to the inverse.<\/p>\n<p>That is a lot to take in! Let\u2019s end this video with an example for you to process how to analyze a statement to write the converse, inverse, and contrapositive statements. <\/p>\n<hr>\n<h2><span id=\"Review\" class=\"m-toc-anchor\"><\/span>Review<\/h2>\n<p>\nFor this exercise, don\u2019t worry about whether the statements are true or false. The statement is:<\/p>\n<div class=\"transcriptcallout\">All four-sided plane figures are rectangles.<\/div>\n<p>\n&nbsp;<br \/>\nNow, pause the video and see if you can figure out the converse, inverse, and contrapositive statements. Remember, it helps to first turn our original statement into a conditional statement so you know the hypothesis and conclusion.<\/p>\n<p>Okay, let\u2019s see if you figured it out!<\/p>\n<p>The conditional statement would be: \u201cIf all figures are four-sided planes, then figures are rectangles.\u201d This gave us our hypothesis and conclusion.<\/p>\n<div class=\"transcriptcallout\"><strong>Hypothesis<\/strong>: If figures are all four-sided planes<br \/>\n<strong>Conclusion<\/strong>: Figures are rectangles<\/div>\n<p>\n&nbsp;<br \/>\nHere are the converse, inverse, and contrapositive statements based on the hypothesis and conclusion:<\/p>\n<ul>\n<li><strong>Converse<\/strong>: If figures are rectangles, then figures are all four-sided planes.<\/li>\n<li><strong>Inverse<\/strong>: If figures are NOT all four-sided planes, then they are NOT rectangles.<\/li>\n<li><strong>Contrapositive<\/strong>: If figures are NOT rectangles, then the figures are NOT all four-sided planes.<\/li>\n<\/ul>\n<p>That\u2019s all for this review! Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Converse,_Inverse,_and_Contrapositive_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Converse, Inverse, and Contrapositive Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich statement is NOT considered a conditional statement?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">If you mow the lawn, then I will pay you for your hard work. <\/div><div class=\"PQ\"  id=\"PQ-1-2\">If you pay your power bill, then you will have electricity. <\/div><div class=\"PQ\"  id=\"PQ-1-3\">If you do not buy firewood, then you will be cold.<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">The sun is shining, because it is summer. <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Conditional statements are also considered \u201cIf-Then\u201d statements. An \u201cIf-Then\u201d statement consists of a hypothesis (if) and a conclusion (then). For example, <em>If<\/em> it is snowing, <em>then<\/em> it is cold. The logic structure of conditional statements is helpful for deriving converse, inverse, and contrapositive statements. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the <em>inverse<\/em> statement of the following conditional statement?<br \/>\nIf it is snowing, then it is cold. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">If it is not snowing, then it is cold.<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">If it is not snowing, then it is not cold.<\/div><div class=\"PQ\"  id=\"PQ-2-3\">If it is cold, then it might be snowing.<\/div><div class=\"PQ\"  id=\"PQ-2-4\">If it is cold, then it is not warm.<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>An <strong>inverse statement<\/strong> assumes the opposite of each of the original statements. The opposite of \u201cIf it is snowing\u201d would be \u201cIf it is not snowing.\u201d The opposite of \u201cthen it is cold\u201d would be \u201cthen it is not cold.\u201d<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the <em>contrapositive<\/em> statement for the following conditional statement?<br \/>\nIf it is a triangle, then it is a polygon. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">If it is not a triangle, then it is not a polygon. <\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">If it is not a polygon, then it is not a triangle. <\/div><div class=\"PQ\"  id=\"PQ-3-3\">If it is a triangle, then it is a polygon. <\/div><div class=\"PQ\"  id=\"PQ-3-4\">If it is a polygon, it is a triangle. <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A <strong>contrapositive statement<\/strong> occurs when you switch the hypothesis and the conclusion in a statement, and negate both statements. In this example, when we switch the hypothesis and the conclusion, and negate both, the result is: If it is not a polygon, then it is not a triangle.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nIdentify \\(p\\) (hypothesis) and \\(q\\) (conclusion) in the following conditional statement:<\/p>\n<div class=\"yellow-math-quote\">If a figure is a triangle, then it has three angles.<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(q\\): If a figure is a triangle<br>\r\n\\(p\\): Then it has congruent angles <\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(p\\): A figure is a polygon<br>\r\n\\(q\\): Can have three angles <\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(p\\): If a figure is not a triangle<br>\r\n\\(q\\): Then it does not have three angles <\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">\\(p\\): If a figure is a triangle<br>\r\n\\(q\\): Then it has three angles <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The hypothesis (\\(p\\)) of a conditional statement is the \u201cif\u201d portion. The conclusion (\\(q\\)) of a conditional statement is the \u201cthen\u201d portion.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich item shows the math statements matched with the correct logic symbols? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">Conditional Statement: \\(q \\rightarrow p\\)<br>\r\nConverse: \\(q \\rightarrow p\\)<br>\r\nInverse: \\(\\sim p \\rightarrow \\sim q\\) <br>\r\nContrapositive: \\(\\sim p \\rightarrow \\sim q\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">Conditional Statement: \\(p \\rightarrow q\\)<br>\r\nConverse: \\(q \\rightarrow p\\)<br>\r\nInverse: \\(\\sim p \\rightarrow \\sim q\\) <br>\r\nContrapositive: \\(\\sim q \\rightarrow \\sim p\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">Conditional Statement: \\(r \\rightarrow t\\)<br>\r\nConverse: \\(q \\rightarrow p\\)<br>\r\nInverse: \\(\\sim t \\rightarrow \\sim r\\) <br>\r\nContrapositive: \\(\\sim q \\rightarrow \\sim p\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">Conditional Statement: \\(p \\rightarrow q\\)<br>\r\nConverse: \\(q \\rightarrow p\\)<br>\r\nInverse: \\(p \\rightarrow q\\) <br>\r\nContrapositive: \\(\\sim h \\rightarrow \\sim c\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The conditional statement is written as \\(p \\rightarrow q\\).<\/p>\n<p>The converse switches the order of the conditional, becoming \\(q \\rightarrow p\\).<\/p>\n<p>The inverse negates both parts of the conditional, giving \\(\\sim p \\rightarrow \\sim q\\).<\/p>\n<p>The contrapositive both switches the order <em>and<\/em> negates both parts, giving \\(\\sim q \\rightarrow \\sim p\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/basic-arithmetic\/\">Return to Basic Arithmetic Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Basic Arithmetic Videos<\/p>\n","protected":false},"author":1,"featured_media":100312,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-7664","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-conversions","7":"page_category-math-advertising-group","8":"page_category-video-pages-for-study-course-sidebar-ad","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/7664","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=7664"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/7664\/revisions"}],"predecessor-version":[{"id":279559,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/7664\/revisions\/279559"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100312"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=7664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}