Question

The last column in the truth table of the statement pattern \( [\text{p} \rightarrow (\text{q} \land \sim \text{p})] \lor [(\text{p} \lor \sim \text{q}) \land \text{p}] \) is

• A. TTTF
• B. TFFF
• C. TTTT
• D. FFTT

Hint:

If a statement is a Tautology, its truth table column is always all T's.

Answer 1

The Correct Option is C

Step 1: Concept A truth table analyzes the truth values of a compound statement for all possible values of its components.

Step 2: Meaning We evaluate the two main brackets separately and then apply the OR (\(\lor\)) operation.

Step 3: Analysis Let's check specific cases: If \(p=T, q=T\): \([T \rightarrow (T \land F)] \lor [(T \lor F) \land T] = [T \rightarrow F] \lor [T \land T] = F \lor T = T\).
If \(p=F, q=T\): \([F \rightarrow (T \land T)] \lor [(F \lor F) \land F] = [F \rightarrow T] \lor [F \land F] = T \lor F = T\).
Similar evaluation for other cases shows the result is always True.

Step 4: Conclusion The pattern is a tautology, so the last column is TTTT. Final Answer: (C)