Question

Suppose that ¬p → ¬q is known to be false. Give the truth values for:

p ∧ q
p ∨ q
p → q

Answer 1

If not p implies not q is false, then, because if the premise of a conditional statement is false, the statement automatically become true, not p can never be false. Therefore, not p is always true. And it follows that if not p is always true, and the overall proposition is false, not q must be false. Or q must be true.

Using this logic, I'm sure you could construct a truth table to solve.