{"id":1918,"date":"2017-03-20T03:05:18","date_gmt":"2017-03-20T03:05:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1918"},"modified":"2017-04-19T18:40:21","modified_gmt":"2017-04-19T18:40:21","slug":"introduction-introduction-to-logic","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/chapter\/introduction-introduction-to-logic\/","title":{"raw":"Introduction: Logic Basics","rendered":"Introduction: Logic Basics"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nIntroduction to Logic\r\n<ul>\r\n \t<li>Combine sets using Boolean logic, using proper notations<\/li>\r\n \t<li>Use statements and conditionals to write and interpret expressions<\/li>\r\n \t<li>Use a truth table to interpret complex statements or conditionals<\/li>\r\n \t<li>Write truth tables given a logical implication, and it\u2019s related\u00a0statements \u2013 converse, inverse, and contrapositive<\/li>\r\n \t<li>Determine whether two statements are logically equivalent<\/li>\r\n \t<li>Use DeMorgan\u2019s laws to define logical equivalences of a statement<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn this section, we will learn how to construct logical statements. We will later combine our knowledge of sets with what we will learn about constructing logical statements to analyze arguments with logic.\r\n\r\nLogic is a systematic way of thinking that allows us to deduce new information\u00a0from old information and to parse the meanings of sentences.\u00a0You use logic informally in everyday life and certainly also in doing mathematics.\u00a0For example, suppose you are working with a certain circle, call it\u00a0\u201cCircle X,\u201d and you have available the following two pieces of information.\r\n<ol>\r\n \t<li>Circle X has radius equal to 3.<\/li>\r\n \t<li>If any circle has radius [latex]r[\/latex], then its area is [latex]\\pi{r}^{2}[\/latex]\u00a0square units.<\/li>\r\n<\/ol>\r\nYou have no trouble putting these two facts together to get:\r\n<ol start=\"3\">\r\n \t<li>Circle X has area [latex]9\\pi[\/latex] square units.<\/li>\r\n<\/ol>\r\nYou are using logic to combine existing information to\u00a0produce new information. Since a major objective in mathematics is to\u00a0deduce new information, logic must play a fundamental role. This chapter\u00a0is intended to give you a sufficient mastery of logic.\r\n\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Introduction to Logic<\/p>\n<ul>\n<li>Combine sets using Boolean logic, using proper notations<\/li>\n<li>Use statements and conditionals to write and interpret expressions<\/li>\n<li>Use a truth table to interpret complex statements or conditionals<\/li>\n<li>Write truth tables given a logical implication, and it\u2019s related\u00a0statements \u2013 converse, inverse, and contrapositive<\/li>\n<li>Determine whether two statements are logically equivalent<\/li>\n<li>Use DeMorgan\u2019s laws to define logical equivalences of a statement<\/li>\n<\/ul>\n<\/div>\n<p>In this section, we will learn how to construct logical statements. We will later combine our knowledge of sets with what we will learn about constructing logical statements to analyze arguments with logic.<\/p>\n<p>Logic is a systematic way of thinking that allows us to deduce new information\u00a0from old information and to parse the meanings of sentences.\u00a0You use logic informally in everyday life and certainly also in doing mathematics.\u00a0For example, suppose you are working with a certain circle, call it\u00a0\u201cCircle X,\u201d and you have available the following two pieces of information.<\/p>\n<ol>\n<li>Circle X has radius equal to 3.<\/li>\n<li>If any circle has radius [latex]r[\/latex], then its area is [latex]\\pi{r}^{2}[\/latex]\u00a0square units.<\/li>\n<\/ol>\n<p>You have no trouble putting these two facts together to get:<\/p>\n<ol start=\"3\">\n<li>Circle X has area [latex]9\\pi[\/latex] square units.<\/li>\n<\/ol>\n<p>You are using logic to combine existing information to\u00a0produce new information. Since a major objective in mathematics is to\u00a0deduce new information, logic must play a fundamental role. This chapter\u00a0is intended to give you a sufficient mastery of logic.<\/p>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1918\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Introduction and Learning Objectives. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Introduction and Learning Objectives\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"3272ce56-7979-4f7a-8baf-acae8ee560cb","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1918","chapter","type-chapter","status-publish","hentry"],"part":159,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1918","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1918\/revisions"}],"predecessor-version":[{"id":2767,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1918\/revisions\/2767"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/parts\/159"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1918\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/media?parent=1918"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapter-type?post=1918"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/contributor?post=1918"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/license?post=1918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}