Question #315605

1.)Determine if the proposition is satisfiable or not by providing any possible combination of inputs that yields a TRUE result.

(p ∧ q) ∨ (¬p ∧¬q)→r


2.)Prove or disapprove the given proposition using a truth table or rules of logic.

¬(¬p ∧ q) ∨ q ⇔ q → p


1
Expert's answer
2022-03-23T02:13:42-0400

1) Let f(p,q,r) = (p ∧ q) ∨ (¬p ∧¬q)→r, then

f(1,1,1)=(11)(00)1=11=1f(1,1,1)=(1\land 1)\lor (0\land 0)\to 1= 1\to 1=1

So, the proposition is satisfiable


2) by using a truth table



As we can see, the last two columns are not identical, which means the given proposition is false



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