{"id":7909,"date":"2022-05-11T14:28:16","date_gmt":"2022-05-11T08:58:16","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7909"},"modified":"2026-01-18T21:08:56","modified_gmt":"2026-01-18T15:38:56","slug":"what-are-logical-connectives","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-are-logical-connectives\/","title":{"rendered":"What are Logical connectives?"},"content":{"rendered":"\n<p><strong><strong><a href=\"https:\/\/www.britannica.com\/topic\/connective-logic\" target=\"_blank\" rel=\"noreferrer noopener\">Logical connectives<\/a>&#8211; <\/strong><\/strong> <strong>Conjunction- p \u22c0 q<\/strong> Any two propositions can be combined by the word \u201cand\u201d to form a compound proposition called the conjunction of the original propositions. Symbolically,<\/p>\n\n<p><span style=\"color: #000000;\"><a style=\"color: #000000;\" title=\"oyo4d\" href=\"https:\/\/oyo4d.one\/\">oyo4d<\/a><\/span><\/p>\n\n\n\n<p>p\u2227q<\/p>\n\n\n\n<p>Read \u201c<em>p <\/em>and <em>q<\/em>,\u201d denotes the conjunction of <em>p <\/em>and <em>q<\/em>. Since <em>p <\/em>\u2227<em>q <\/em>is a proposition it has a truth value, and this truth<\/p>\n\n\n\n<p>Value depends only on the truth values of <em>p <\/em>and <em>q<\/em>.<\/p>\n\n\n\n<p>Note- If <em>p <\/em>and <em>q <\/em>are true, then <em>p <\/em>\u2227<em>q <\/em>is true; otherwise <em>p <\/em>\u2227<em>q <\/em>is false.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>2. Disjunction, p <\/strong><strong>\u2228<\/strong><strong>q<\/strong><\/h2>\n\n\n\n<p>Any two propositions can be combined by the word \u201cor\u201d to form a compound proposition called the disjunction of the original propositions. Symbolically,<\/p>\n\n\n\n<p><em>p<\/em>\u2228<em>q<\/em><\/p>\n\n\n\n<p>Read \u201c<em>p <\/em>or <em>q<\/em>,\u201d denotes the disjunction of <em>p <\/em>and <em>q<\/em>. The truth value of <em>p <\/em>\u2228<em>q <\/em>depends only on the truth values of <em>p<\/em><\/p>\n\n\n\n<p>And <em>q <\/em>as follows-<\/p>\n\n\n\n<p>If p and q are false, then p \u2228q is false; otherwise p \u2228q is true<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Negation<\/strong><\/h2>\n\n\n\n<p>Given any proposition p, another proposition, called the negation of p, can be formed by writing \u201cIt is not true that . . .\u201d or \u201cIt is false that . . .\u201d before p or, if possible, by inserting in p the word \u201cnot.\u201d Symbolically, the negation of p, read \u201cnot p,\u201d is denoted by<\/p>\n\n\n\n<p>\uffe2p<\/p>\n\n\n\n<p>The truth value of \uffe2p depends on the truth value of p as follows-<\/p>\n\n\n\n<p>If p is true, then \uffe2p is false; and if p is false, then \uffe2p is true<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Basic logical operations<\/strong> of <strong>Logical connectives- <\/strong><\/h2>\n\n\n\n<p><strong>Conjunction- p \u22c0 q<\/strong><\/p>\n\n\n\n<p>Any two propositions can be combined by the word \u201cand\u201d to form a compound proposition called the conjunctionof the original propositions. Symbolically,<\/p>\n\n\n\n<p>p\u2227q<\/p>\n\n\n\n<p>Read \u201c<em>p <\/em>and <em>q<\/em>,\u201d denotes the conjunction of <em>p <\/em>and <em>q<\/em>. Since <em>p <\/em>\u2227<em>q <\/em>is a proposition it has a truth value, and this truth<\/p>\n\n\n\n<p>Value depends only on the truth values of <em>p <\/em>and <em>q<\/em>.<\/p>\n\n\n\n<p>Note- If <em>p <\/em>and <em>q <\/em>are true, then <em>p <\/em>\u2227<em>q <\/em>is true; otherwise <em>p <\/em>\u2227<em>q <\/em>is false.<\/p>\n\n\n\n<p><strong>2. Disjunction, p <\/strong><strong>\u2228<\/strong><strong>q<\/strong><\/p>\n\n\n\n<p>Any two propositions can be combined by the word \u201cor\u201d to form a compound proposition called the disjunctionof the original propositions. Symbolically,<\/p>\n\n\n\n<p><em>p<\/em>\u2228<em>q<\/em><\/p>\n\n\n\n<p>Read \u201c<em>p <\/em>or <em>q<\/em>,\u201d denotes the disjunction of <em>p <\/em>and <em>q<\/em>. The truth value of <em>p <\/em>\u2228<em>q <\/em>depends only on the truth values of <em>p<\/em><\/p>\n\n\n\n<p>And <em>q <\/em>as follows-<\/p>\n\n\n\n<p>If p and q are false, then p \u2228q is false; otherwise p \u2228q is true<\/p>\n\n\n\n<p><strong>Negation-<\/strong><\/p>\n\n\n\n<p>Given any proposition p, another proposition, called the negation of p, can be formed by writing \u201cIt is not true that . . .\u201d or \u201cIt is false that . . .\u201d before p or, if possible, by inserting in p the word \u201cnot.\u201d Symbolically, the negation of p, read \u201cnot p,\u201d is denoted by<\/p>\n\n\n\n<p>\uffe2p<\/p>\n\n\n\n<p>The truth value of \uffe2p depends on the truth value of p as follows-If p is true, then \uffe2p is false; and if p is false, then \uffe2p is true<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Logical connectives&#8211; Conjunction- p \u22c0 q Any two propositions can be combined by the word \u201cand\u201d to form a compound proposition called&hellip;<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-7909","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What are Logical connectives? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"Logical connectives- Any two propositions can be combined by the word \u201cand\u201d to form a compound proposition called the conjunction of the original propositions. 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