{"id":6789,"date":"2021-12-30T21:39:57","date_gmt":"2021-12-30T21:39:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=6789"},"modified":"2024-06-15T01:15:47","modified_gmt":"2024-06-15T01:15:47","slug":"1-7-truth-tables-negation-conjunction-disjunction","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/1-7-truth-tables-negation-conjunction-disjunction\/","title":{"raw":"1.7 Truth Tables: Negation, Conjunction, Disjunction","rendered":"1.7 Truth Tables: Negation, Conjunction, Disjunction"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>What is a Truth Table?<\/li>\r\n \t<li>Basic Truth Tables for\r\n<ul>\r\n \t<li>Negation<\/li>\r\n \t<li>Conjunction<\/li>\r\n \t<li>Disjunction<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Order of Logical Operations\r\n<ul>\r\n \t<li>Putting together (negation, conjunction, disjunction)<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\nBecause complex statements can get tricky to think about, we can create a <strong>truth table<\/strong> to break the complex statement into\u00a0simple statements, and determine whether they are true or false. A table will help keep track of all the truth values of the simple statements that make up a complex statement, leading to an analysis of the full statement.\r\n<div class=\"textbox\">\r\n<h3>Truth Table<\/h3>\r\nA table showing what the resulting truth value of a complex statement is for all the possible truth values for the simple statements.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSuppose you\u2019re picking out a new couch, and your significant other says \u201cget a sectional <em>or<\/em> something with a chaise.\u201d Construct a truth table that describes the elements of the conditions of this statement and whether the conditions are met.\r\n[reveal-answer q=\"14714\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"14714\"]\r\n\r\nThis is a complex statement made of two simpler conditions: \u201cis a sectional,\u201d and \u201chas a chaise.\u201d For simplicity, let\u2019s use <em>S<\/em> to designate \u201cis a sectional,\u201d and <em>C<\/em> to designate \u201chas a chaise.\u201d The condition <em>S<\/em> is true if the couch is a sectional.\r\n\r\nA truth table for this would look like this:\r\n<table>\r\n<thead>\r\n<tr>\r\n<th><em>S<\/em><\/th>\r\n<th><em>C<\/em><\/th>\r\n<th><em>S<\/em> or\u00a0<em>C<\/em><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn the table, T is used for true, and F for false. In the first row, if <em>S<\/em> is true and <em>C<\/em> is also true, then the complex statement \u201c<em>S <\/em>or<em> C<\/em>\u201d is true. This would be a sectional that also has a chaise, which meets our desire.\r\n\r\nRemember also that <em>or<\/em> in logic is not exclusive; if the couch has both features, it does meet the condition.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<b>Negation<\/b>\u00a0tells us, \u201cIt is not the case that\u2026 \u201d\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165626\/Negation.png\"><img class=\"size-medium wp-image-6885 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165626\/Negation-300x203.png\" alt=\"\" width=\"300\" height=\"203\" \/><\/a>\r\n\r\n<b>Conjunction<\/b>\u00a0tells us, \u201cBoth\u2026 are the case.\u201d Conjunctions are only true when both conjuncts are true.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02170039\/Conjunction.png\"><img class=\"size-medium wp-image-6887 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02170039\/Conjunction-300x221.png\" alt=\"\" width=\"300\" height=\"221\" \/><\/a>\r\n\r\n<b style=\"font-size: 1rem; text-align: initial;\">Disjunction<\/b><span style=\"font-size: 1rem; text-align: initial;\">\u00a0tells us that, \u201cAt least one is the case\u2026 \u201d Disjunctions are only false when both disjuncts are false.<\/span>\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165915\/Disjunction.png\"><img class=\"size-medium wp-image-6886 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165915\/Disjunction-300x221.png\" alt=\"\" width=\"300\" height=\"221\" \/><\/a>\r\n<div class=\"textbox\">\r\n<h3>Basic Truth Tables<\/h3>\r\nNotice that the b column has the pattern TFTF. Then the A column has the pattern TTFF.\r\n<table width=\"40%&quot;\">\r\n<thead>\r\n<tr>\r\n<th>a<\/th>\r\n<th>b<\/th>\r\n<th>[latex]a\\wedge{b}[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox\">When thinking of \"and\" situations, it is often helpful to imagine a scenario. Imagine you are a renter and you made an agreement with your landlord. You agreed that you would take out the trash AND mow the lawn. Now, if A is take out the trash and B is mow the lawn, you only hold up your end of the deal when you do both. The truth values will be false except when you do both, in which case it will be true.<\/div>\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>a<\/th>\r\n<th>b<\/th>\r\n<th>[latex]a\\vee{b}[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox\">\r\n\r\nWhen thinking of \"or\" situations, it is also helpful to think of a scenario. Imagine you are a renter (like in the previous example) and your landlord asked you to pay on the 1st of pay on the 2nd. Suppose A is pay on the first and B is pay on the second. The result will be true in each scenario except when\u00a0 you don't pay on the 1st or on the second. In that case the result is false.\r\n\r\nTruth tables for \"or\" use the \"<strong>inclusive or<\/strong>\", meaning A or B or both. For example: You can A (bring your umbrella) or B (wear a rain coat) or both (bring your umbrella and wear a rain coat). \"<strong>Exclusive or<\/strong>\", on the other hand, means A or B, but not both. For example, you can A (take your lottery winnings in one lump sum) or B (take you lottery winnings as monthly payments), but you cannot do both.\r\n\r\n<\/div>\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>a<\/th>\r\n<th>[latex]\\sim{a}[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>T<\/td>\r\n<td>F<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>F<\/td>\r\n<td>T<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox\">I just think of opposite day when it comes to negations. Everything is opposite of what it was to begin with.<\/div>\r\n<strong>Note:<\/strong>\r\n\r\nWhen we create the truth table, we need to list all the possible truth value combinations for A and B. Notice how the first column contains 2 True's (T) followed by 2 False's (F). The second column alternates T, F, T, F. This pattern ensures that all 4 combinations are considered.\r\n<table style=\"border-collapse: collapse; width: 0%; height: 119px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 1.66945%; text-align: center;\"><strong>A<\/strong><\/td>\r\n<td style=\"width: 1.66945%; text-align: center;\"><strong>B<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\r\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\r\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\r\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\r\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]25467[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/strong><\/span><\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>What is a Truth Table?<\/li>\n<li>Basic Truth Tables for\n<ul>\n<li>Negation<\/li>\n<li>Conjunction<\/li>\n<li>Disjunction<\/li>\n<\/ul>\n<\/li>\n<li>Order of Logical Operations\n<ul>\n<li>Putting together (negation, conjunction, disjunction)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<p>Because complex statements can get tricky to think about, we can create a <strong>truth table<\/strong> to break the complex statement into\u00a0simple statements, and determine whether they are true or false. A table will help keep track of all the truth values of the simple statements that make up a complex statement, leading to an analysis of the full statement.<\/p>\n<div class=\"textbox\">\n<h3>Truth Table<\/h3>\n<p>A table showing what the resulting truth value of a complex statement is for all the possible truth values for the simple statements.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Suppose you\u2019re picking out a new couch, and your significant other says \u201cget a sectional <em>or<\/em> something with a chaise.\u201d Construct a truth table that describes the elements of the conditions of this statement and whether the conditions are met.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q14714\">Show Solution<\/span><\/p>\n<div id=\"q14714\" class=\"hidden-answer\" style=\"display: none\">\n<p>This is a complex statement made of two simpler conditions: \u201cis a sectional,\u201d and \u201chas a chaise.\u201d For simplicity, let\u2019s use <em>S<\/em> to designate \u201cis a sectional,\u201d and <em>C<\/em> to designate \u201chas a chaise.\u201d The condition <em>S<\/em> is true if the couch is a sectional.<\/p>\n<p>A truth table for this would look like this:<\/p>\n<table>\n<thead>\n<tr>\n<th><em>S<\/em><\/th>\n<th><em>C<\/em><\/th>\n<th><em>S<\/em> or\u00a0<em>C<\/em><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In the table, T is used for true, and F for false. In the first row, if <em>S<\/em> is true and <em>C<\/em> is also true, then the complex statement \u201c<em>S <\/em>or<em> C<\/em>\u201d is true. This would be a sectional that also has a chaise, which meets our desire.<\/p>\n<p>Remember also that <em>or<\/em> in logic is not exclusive; if the couch has both features, it does meet the condition.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><b>Negation<\/b>\u00a0tells us, \u201cIt is not the case that\u2026 \u201d<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165626\/Negation.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-6885 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165626\/Negation-300x203.png\" alt=\"\" width=\"300\" height=\"203\" \/><\/a><\/p>\n<p><b>Conjunction<\/b>\u00a0tells us, \u201cBoth\u2026 are the case.\u201d Conjunctions are only true when both conjuncts are true.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02170039\/Conjunction.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-6887 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02170039\/Conjunction-300x221.png\" alt=\"\" width=\"300\" height=\"221\" \/><\/a><\/p>\n<p><b style=\"font-size: 1rem; text-align: initial;\">Disjunction<\/b><span style=\"font-size: 1rem; text-align: initial;\">\u00a0tells us that, \u201cAt least one is the case\u2026 \u201d Disjunctions are only false when both disjuncts are false.<\/span><\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165915\/Disjunction.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-6886 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/12\/02165915\/Disjunction-300x221.png\" alt=\"\" width=\"300\" height=\"221\" \/><\/a><\/p>\n<div class=\"textbox\">\n<h3>Basic Truth Tables<\/h3>\n<p>Notice that the b column has the pattern TFTF. Then the A column has the pattern TTFF.<\/p>\n<table style=\"width: 40%&quot;\">\n<thead>\n<tr>\n<th>a<\/th>\n<th>b<\/th>\n<th>[latex]a\\wedge{b}[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox\">When thinking of &#8220;and&#8221; situations, it is often helpful to imagine a scenario. Imagine you are a renter and you made an agreement with your landlord. You agreed that you would take out the trash AND mow the lawn. Now, if A is take out the trash and B is mow the lawn, you only hold up your end of the deal when you do both. The truth values will be false except when you do both, in which case it will be true.<\/div>\n<table>\n<thead>\n<tr>\n<th>a<\/th>\n<th>b<\/th>\n<th>[latex]a\\vee{b}[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox\">\n<p>When thinking of &#8220;or&#8221; situations, it is also helpful to think of a scenario. Imagine you are a renter (like in the previous example) and your landlord asked you to pay on the 1st of pay on the 2nd. Suppose A is pay on the first and B is pay on the second. The result will be true in each scenario except when\u00a0 you don&#8217;t pay on the 1st or on the second. In that case the result is false.<\/p>\n<p>Truth tables for &#8220;or&#8221; use the &#8220;<strong>inclusive or<\/strong>&#8220;, meaning A or B or both. For example: You can A (bring your umbrella) or B (wear a rain coat) or both (bring your umbrella and wear a rain coat). &#8220;<strong>Exclusive or<\/strong>&#8220;, on the other hand, means A or B, but not both. For example, you can A (take your lottery winnings in one lump sum) or B (take you lottery winnings as monthly payments), but you cannot do both.<\/p>\n<\/div>\n<table>\n<thead>\n<tr>\n<th>a<\/th>\n<th>[latex]\\sim{a}[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>T<\/td>\n<td>F<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox\">I just think of opposite day when it comes to negations. Everything is opposite of what it was to begin with.<\/div>\n<p><strong>Note:<\/strong><\/p>\n<p>When we create the truth table, we need to list all the possible truth value combinations for A and B. Notice how the first column contains 2 True&#8217;s (T) followed by 2 False&#8217;s (F). The second column alternates T, F, T, F. This pattern ensures that all 4 combinations are considered.<\/p>\n<table style=\"border-collapse: collapse; width: 0%; height: 119px;\">\n<tbody>\n<tr>\n<td style=\"width: 1.66945%; text-align: center;\"><strong>A<\/strong><\/td>\n<td style=\"width: 1.66945%; text-align: center;\"><strong>B<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\n<td style=\"width: 1.66945%; text-align: center;\">T<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\n<td style=\"width: 1.66945%; text-align: center;\">F<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm25467\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=25467&theme=oea&iframe_resize_id=ohm25467&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/strong><\/span><\/p>\n","protected":false},"author":359705,"menu_order":9,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-6789","chapter","type-chapter","status-publish","hentry"],"part":159,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6789","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/users\/359705"}],"version-history":[{"count":18,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6789\/revisions"}],"predecessor-version":[{"id":7055,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6789\/revisions\/7055"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/parts\/159"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6789\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/media?parent=6789"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapter-type?post=6789"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/contributor?post=6789"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/license?post=6789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}