{"id":14376,"date":"2016-02-16T17:58:26","date_gmt":"2016-02-16T17:58:26","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=14376"},"modified":"2016-02-16T17:58:26","modified_gmt":"2016-02-16T17:58:26","slug":"math-comp-sci-symbolic-logic-contradiction","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-comp-sci-symbolic-logic-contradiction\/","title":{"rendered":"Math & Comp Sci: Symbolic Logic: contradiction"},"content":{"rendered":"

The tutor defines, in the context of symbolic logic, contradiction, with a couple of examples.<\/h1>\n

For those new to symbolic logic, my previous post<\/a> leads back to others that will fill the gaps.<\/p>\n

A contradiction is a compound statement that is always false. The fundamental example is p ∧ ¬ p, which must be a contradiction, since both p and “not p” can’t be true simultaneously.<\/p>\n

Here is a second contradiction:<\/p>\n

(p ⊻ q) ∧ (p ∧ q)<\/p>\n

p ⊻ q is only true when one of p,q is true, but not both. However, both<\/em> p,q must be true for p ∧ q to be. Therefore, the bracketed statements can’t be true simultaneously, meaning that the central “and” will always be false.<\/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 defines, in the context of symbolic logic, contradiction, with a couple of examples. For those new to symbolic logic, my previous post leads back to others that will fill the gaps. A contradiction is a compound statement that …<\/p>\n

Math & Comp Sci: Symbolic Logic: contradiction<\/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":[1435,1430],"class_list":["post-14376","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-math","tag-contradiction","tag-symbolic-logic"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14376","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=14376"}],"version-history":[{"count":15,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14376\/revisions"}],"predecessor-version":[{"id":14391,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/14376\/revisions\/14391"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=14376"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=14376"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=14376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}