{"id":14331,"date":"2016-02-13T19:06:55","date_gmt":"2016-02-13T19:06:55","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=14331"},"modified":"2016-02-13T19:06:55","modified_gmt":"2016-02-13T19:06:55","slug":"math-logic-what-is-a-tautology","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-logic-what-is-a-tautology\/","title":{"rendered":"Math: logic: what is a tautology?"},"content":{"rendered":"

The tutor continues about logic, defining tautology with an example.<\/h1>\n

In yesterday’s post<\/a> I began about symbolic logic.<\/p>\n

A tautology is a compound statement that is always true. For an example, consider the following two statements:<\/p>\n

    \n
  1. p: Today it will rain.<\/li>\n
  2. q: Today it won’t rain.<\/li>\n<\/ol>\n

    The compound statement p ∨ q, based on the values for p, q, above, is always true. Therefore, in this case, p ∨ q is a tautology. The fundamental reason why is that q is opposite of p: q = ¬ p.<\/p>\n

    In any case, p will either happen or it won’t; therefore, p ∨ ¬p is a tautology. Generally, for any statement x, x ∨ ¬ x is a tautology.<\/p>\n

    Source:<\/p>\n

    Grimaldi, Ralph P. Discrete and Combinatorial Mathematics<\/u>. Don Mills: Addison-
      Wesley, 1994.<\/p>\n

    Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

    The tutor continues about logic, defining tautology with an example. In yesterday’s post I began about symbolic logic. A tautology is a compound statement that is always true. For an example, consider the following two statements: p: Today it will …<\/p>\n

    Math: logic: what is a tautology?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[105,3],"tags":[1430,1431],"class_list":["post-14331","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-math","tag-symbolic-logic","tag-tautology"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14331","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=14331"}],"version-history":[{"count":12,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14331\/revisions"}],"predecessor-version":[{"id":14343,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14331\/revisions\/14343"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=14331"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=14331"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=14331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}