Question

Given the conditional statement-p → 9, which statement is logically equivalent?

a) p → ~9
b) ~p → ~9
c) ~9 → ~p
d) ~9 → p

Answer 1

The logically equivalent statement for p → 9 is p → ~9.

Step-by-step explanation:

The logically equivalent statement for p → 9 is ~(~p) → 9.

To understand why, we can use the logical equivalence laws. The law that applies in this case is the negation of implication ~(p → q) ≡ p ∧ ~q.

So, in this case, it becomes ~(p → 9) ≡ p ∧ ~9. Since 9 is always true, ~9 is always false, making the expression equivalent to ~p, which translates to option a) p → ~9.