If p and q are both true, then which of the following statements has the same truth-value as ~p → q? a) ~p ∧ ~q b) ~p ∨ ~q c) p ∧ ~q d) ~q → p

If p and q are both true, then

is an implication of the form

which is true, because every implication starting with false is true, i.e.

So, we're looking for an expression evaluating to true. Let's see what we have:

A) is an AND proposition. Logical AND is true only if both parts are true. So, you have

So it's not the right option.

B) is an OR proposition. Logical OR is true whenever one of the two parts is true. So, you have

So it's not the right option.

C) is again an AND proposition. You have

So this is not the right option.

D) Finally, the last one is again an implication, and again it starts with false:

So this is true, and thus is the correct option.

i need the options

step-by-step explanation: