Answer to Question #182230 in Discrete Mathematics for jhon

Question #182230

Prove that (p ∧ q) → (p ∨ q) is a tautology using the table of propositional

equivalences.


1
Expert's answer
2021-05-02T08:52:18-0400

Using the following equivalence law (you can prove from a truth table):

rs¬rsr\rightarrow s\equiv \lnot r\lor s

Let r=pqr = p\land q and s=pqs = p\lor q, then

(pq)(pq)¬(pq)(pq).(p\land q)\rightarrow (p\lor q)\equiv \lnot(p\land q)\lor(p\lor q).


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