The truth value of the proposition [ q AND (p -> NOT q) ] -> NOT p isQuestion 10Answera.Tautology.b.Contingency.c.Contradiction.d.None of the Given Choices.

To determine the truth value of the proposition $[ q \text{ AND } (p \rightarrow \neg q) ] \rightarrow \neg p$, we will analyze it step by step.

1. Identify the components:

   • $q$
   • $p \rightarrow \neg q$
   • $q \text{ AND } (p \rightarrow \neg q)$
   • $[ q \text{ AND } (p \rightarrow \neg q) ] \rightarrow \neg p$

2. Construct the truth table:

   $p$	$q$	$\neg q$	$p \rightarrow \neg q$	$q \text{ AND } (p \rightarrow \neg q)$	$\neg p$	$[ q \text{ AND } (p \rightarrow \neg q) ] \rightarrow \neg p$
   T	T	F	F	F	F	T
   T	F	T	T	F	F	T
   F	T	F	T	T	T	T
   F	F	T	T	F	T	T

3. Analyze the truth table:

   • In all possible cases (TT, TF, FT, FF), the final column $[ q \text{ AND } (p \rightarrow \neg q) ] \rightarrow \neg p$ is always true.

4. Conclusion:

   • Since the proposition is always true regardless of the truth values of $p$ and $q$, it is a tautology.

Therefore, the answer is: a. Tautology.