Answer to Question #325422 in Discrete Mathematics for aaxl

Question

Suppose that the statement p → ¬q is false. Find all combinations of truth values of r and s for which

(¬q → r) ∧ (¬p ∨ s) is true.

Answer 1

$p\to\neg q = 0 \implies p=1, q=1$

$(0\to r)\land (0 \lor s)=1 \implies(0\to r=1)\land (0\lor s=1)\implies r=0, r=1, s=1$

r can be both 0 and 1, but s can be only 1.