{"id":18495,"date":"2016-10-24T15:59:46","date_gmt":"2016-10-24T15:59:46","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=18495"},"modified":"2016-10-25T19:42:40","modified_gmt":"2016-10-25T19:42:40","slug":"math-symbolic-logic-meets-digital-circuits-p%e2%86%92q-means-%c2%aca-or-b","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-symbolic-logic-meets-digital-circuits-p%e2%86%92q-means-%c2%aca-or-b\/","title":{"rendered":"Math: symbolic logic meets digital circuits: p\u2192q means \u00acA or B"},"content":{"rendered":"

The tutor translates p→q to the boolean expression ¬A or B.<\/h1>\n

In my beginning post about symbolic logic,<\/a> I mention that the statement p implies q, also stated p→q, has the following truth table:<\/p>\n\n\n\n\n\n\n
p<\/td>\nq<\/td>\np→q<\/td>\n<\/tr>\n
0<\/td>\n0<\/td>\n1<\/td>\n<\/tr>\n
0<\/td>\n1<\/td>\n1<\/td>\n<\/tr>\n
1<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
1<\/td>\n1<\/td>\n1<\/td>\n<\/tr>\n<\/table>\n

(I also mention, in that same post,<\/a> the symbols and so on needed to understand basic logical expressions such as the ones herein.)<\/p>\n

In digital logic (aka, digital circuits, boolean expressions, etc), ¬A or B has the same truth table:<\/p>\n\n\n\n\n\n\n
A<\/td>\nB<\/td>\n¬A or B<\/td>\n<\/tr>\n
0<\/td>\n0<\/td>\n1<\/td>\n<\/tr>\n
0<\/td>\n1<\/td>\n1<\/td>\n<\/tr>\n
1<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
1<\/td>\n1<\/td>\n1<\/td>\n<\/tr>\n<\/table>\n

Neat, eh?<\/p>\n

Source:<\/p>\n

Grimaldi, Ralph P. Discrete and Combinatorial Mathematics<\/u>, 3rd ed. Don Mills: Addison-Wesley Publishing Company, 1994.<\/p>\n

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

The tutor translates p→q to the boolean expression ¬A or B. In my beginning post about symbolic logic, I mention that the statement p implies q, also stated p→q, has the following truth table: p q p→q 0 0 1 …<\/p>\n

Math: symbolic logic meets digital circuits: p\u2192q means \u00acA or B<\/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":[3],"tags":[1987,1984,1986,1983,1985,1988,1430],"class_list":["post-18495","post","type-post","status-publish","format-standard","hentry","category-math","tag-binary-expression-for-p-implies-q","tag-boolean-expression-for-p-implies-q","tag-digital-circuit-for-p-implies-q","tag-digital-expression-for-p-implies-q","tag-equivalent-expression-for-p-implies-q","tag-switching-function-for-p-implies-q","tag-symbolic-logic"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18495","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=18495"}],"version-history":[{"count":15,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18495\/revisions"}],"predecessor-version":[{"id":18518,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18495\/revisions\/18518"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=18495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=18495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=18495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}