{"id":6849,"date":"2014-03-24T15:44:16","date_gmt":"2014-03-24T15:44:16","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6849"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-introduction-to-logic-and-algebra","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/03\/24\/math-introduction-to-logic-and-algebra\/","title":{"rendered":"Math Introduction to Logic and Algebra"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Some of the relationships that are central to algebraic reasoning are also important to logical reasoning.\u00a0 While algebra deals with numbers and variables that are linked together in relationships called equations, logic deals with statements that are linked in relationships called propositions.\u00a0 Just as open sentences can be true or false by their solutions, conditional statements can be true or false.<\/p>\n

What Are Conditional Statements?<\/strong><\/p>\n

Conditional statements are also called \u201cif-then\u201d statements.\u00a0 A statement such as \u201cIf the sun is shining, then I cast a shadow\u201d has two parts, \u201cthe sun is shining\u201d and \u201cI cast a shadow.\u201d\u00a0 Similarly, \u201cIf 6 is an even number, then 6 is evenly divisible by 2,\u201d has two parts, \u201c6 is an even number\u201d and \u201c6 is evenly divisible by 2.\u201d<\/p>\n

When Is A Conditional Statement True?<\/strong><\/p>\n

A conditional statement is true if both parts of the statement are true.\u00a0 For example, \u201cIf the sun is shining\u201d then \u201cI cast a shadow\u201d is true.\u00a0 In addition, a conditional statement is true if both parts of the statement are false.\u00a0 Suppose it is actually dark, so that \u201cthe sun is shining\u201d is false.\u00a0 Then, \u201cI cast a shadow\u201d is also false.<\/p>\n

When Is a Conditional Statement False?<\/strong><\/p>\n

Suppose the first part of the statement is true, and the sun is shining.\u00a0 However, I didn\u2019t cast a shadow.\u00a0 The statement would be false.\u00a0 Similarly, if x is an even number but x is actually not evenly divisible by 2, the statement is false.<\/p>\n

What Is the Converse of a Statement?<\/strong><\/p>\n

The converse of a statement is when the first part of the statement and the second part are reversed. Suppose the statement is \u201cIf x is a rose, then x is a flower.\u201d\u00a0 Its converse is \u201cIf x is a flower, then x is a rose.\u00a0 Notice that the statement is true because a rose is a flower.\u00a0 However, its converse is not necessarily true.\u00a0 Suppose the flower were a daisy.\u00a0 A daisy is a flower (true), but a daisy is not also a rose.<\/p>\n

What Is the Relationship to Equations?<\/strong><\/p>\n

An algebra equation is a statement of conditions in numerical form.\u00a0 In order to find a solution, both parts need to balance.\u00a0 For example, suppose 2x + 6 = 8.\u00a0 In order to make both statements true, 2x = 8 – 6 or 2x = 2, so x = 1.\u00a0 When the equation is checked 2 \u2219 1 + 6 = 8.<\/p>\n

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Overview: Some of the relationships that are central to algebraic reasoning are also important to logical reasoning.\u00a0 While algebra deals with numbers and variables that are linked together in relationships called equations, logic deals with statements that are linked in relationships called propositions.\u00a0 Just as open sentences can be true or false by their solutions, […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[371,2646],"class_list":["post-6849","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-conditional-statements","tag-converse"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6849","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6849"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6849\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6849"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6849"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6849"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}