[ NOT(p AND q) AND (NOT p OR q) AND (NOT q OR q) ] AND pisQuestion 4Answera.T.b.F.c.q.d.NOT q.e.None of the Given Choices.f.p.g.NOT p.

Sure, let's break down the given expression step by step:

1. The expression is: [ NOT(p AND q) AND (NOT p OR q) AND (NOT q OR q) ] AND p

2. Let's simplify each part inside the brackets first:

   • NOT(p AND q): This is the negation of the conjunction of p and q. According to De Morgan's laws, this is equivalent to NOT p OR NOT q.
   • NOT p OR q: This is already in its simplest form.
   • NOT q OR q: This is a tautology because q OR NOT q is always true.

3. Now, substitute the simplified parts back into the expression:

   • [ (NOT p OR NOT q) AND (NOT p OR q) AND true ] AND p

4. Since true does not affect the conjunction, we can simplify further:

   • [ (NOT p OR NOT q) AND (NOT p OR q) ] AND p

5. Distribute the AND inside the brackets:

   • [(NOT p OR NOT q) AND (NOT p OR q)]

6. Let's analyze the expression (NOT p OR NOT q) AND (NOT p OR q):

   • This can be simplified by considering the possible values of p and q:

     • If p is true, then NOT p is false, so the expression depends on q.
     • If q is true, then NOT q is false, so the expression depends on p.

   • The expression (NOT p OR NOT q) AND (NOT p OR q) simplifies to NOT p.

7. Now, substitute back into the main expression:

   • [ NOT p ] AND p

8. This simplifies to:

   • NOT p AND p

9. NOT p AND p is always false because p and NOT p cannot be true at the same time.

Therefore, the answer is:

b. F.