Answer to Question #278249 in Discrete Mathematics for tom

Question

If the statement q ^ r is true, determine all combinations of truth values for p and s such that the statement (q -> [¬p v s]) ^ [¬s -> r] is true.

Answer 1

$q \land r$ is true, so q = true and r = true.

$(q \to (\lnot p \lor s))$ is true if $(\lnot p \lor s)$ is true, which happens in all combination apart from p=true and s=false.

$(\lnot s \to r) =(s \lor r)$, since r=true, this statement always true. So following truth values make statement true - p = true and s = true, p=false and s=true, p=false and s=false.