Question

Prove [(p∧q) → r] → [(p→r)⋁(q→r)] is a tautology without using a truth table.

Answer 1

what other method do you use other than truth table?

Answer 2

I am not sure. I think we are supposed to use logical equivalences.. Demorgan laws, implication law, etc

Answer 3

thats why I am asking for help on here

Answer 4

hello?

Answer 5

left side:\[=\neg r \to\neg ( p \wedge q)\]\[=\neg r \to (\neg p \vee \neg q)\]

right side:\[= \left( \neg r \to \neg p \right) \vee \left( \neg r \to \neg q \right)\]

Answer 6

just using implication and deMorgan