The simplification of[ 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 simplify the given expression step by step:

The expression is: $[ \neg(p \land q) \land (\neg p \lor q) \land (\neg q \lor q) ] \land p$

1. Simplify $\neg q \lor q$: $\neg q \lor q$ is always true (T) because either $q$ is true or $\neg q$ is true.

   So, the expression becomes: $[ \neg(p \land q) \land (\neg p \lor q) \land T ] \land p$

2. Since $\neg q \lor q$ is true, it does not affect the AND operation: $[ \neg(p \land q) \land (\neg p \lor q) ] \land p$

3. Simplify $\neg(p \land q)$: $\neg(p \land q)$ is equivalent to $\neg p \lor \neg q$ (De Morgan's law).

   So, the expression becomes: $[ (\neg p \lor \neg q) \land (\neg p \lor q) ] \land p$

4. Distribute $\land$ over $\lor$: $(\neg p \lor \neg q) \land (\neg p \lor q)$

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

   • If $p$ is true, $\neg p$ is false, so the expression depends on $q$: $\neg q \land q$ which is false.
   • If $p$ is false, $\neg p$ is true, so the expression is true regardless of $q$.

   Therefore, the expression simplifies to: $\neg p$

5. Combine with the outer $\land p$: $\neg p \land p$

   This is always false because $p$ and $\neg p$ cannot be true at the same time.

So, the final simplified expression is: $\text{False (F)}$

The correct answer is: b. F