Answer to Question #346072 in Discrete Mathematics for Nam Sae

Question #346072

Show that (~π’‘βˆ¨π’’)∧(π’‘βˆ§~𝒒) is a contradiction.



1
Expert's answer
2022-05-31T12:35:32-0400

"(\\sim p\\lor q)\\land (p\\land \\sim q)"


"(\\sim p\\lor q)\\land p\\land \\sim q" , associative law

"\\big((\\sim p\\land p)\\lor(q\\land p)\\big)\\land \\sim q" , distributive law

"(F\\lor (q\\land p))\\land \\sim q" , negation law

"(q\\land p)\\land \\sim q" , identity law

"(q\\land \\sim q)\\land p" , associative law

"F\\land p" , negation law

"F" , domination law


It is a contradiction


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