Question

Let "A = (¬p) ∨ (¬q)" and "B = ¬(p ∨ q)." Then the truth values of "A" and "B" are the same.

Answer 1

Yes, the truth values of expressions A = (¬p) ∨ (¬q) and B = ¬(p ∨ q) are the same.

Step-by-step explanation:

Yes, the truth values of expressions A = (¬p) ∨ (¬q) and B = ¬(p ∨ q) are the same.

Step-by-step explanation:

1. Let's find the truth value of A.
2. If either ¬p or ¬q is true, then A is true.
3. If both p and q are false, then ¬p is true and ¬q is true, so A is true.
4. If both p and q are true, then neither ¬p nor ¬q is true, so A is false.
5. Similarly, let's find the truth value of B.
6. If p or q is true, then B is false.
7. If both p and q are false, then ¬p is true and ¬q is true, so B is true.
8. As you can see, A and B have the same truth values.