Answer to Question #315605 in Discrete Mathematics for Kenji

Question

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

Answer 1

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

$f(1,1,1)=(1\land 1)\lor (0\land 0)\to 1= 1\to 1=1$

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