Answer
see step by step work option
Work Step by Step
To show that these are not logically equivalent,
we need only find one assignment of truth values to p, q, r, and s for which the truth values of (p _, q) _, (r _, s) and (p _, r) _, (q _, s) differ
. Let us try to make the first one false.
That means we have to make r _, s false, so we want r to be true and s to be false.
If we let p and q be false, then each of the other three simple conditional statements (p _, q, p _, r, and q _, s) will be true.
Then (p-t q) _, (r _, s) will be T-t F, which is false; but (p-t r) _, (q _, s) will be T-t T, which is true.
