Question

Which of the following statement is not tautology?

• A. \(\sim(p \land q) \lor p\)
• B. \((p \land q) \rightarrow p\)
• C. \(q \lor \sim(p \land q)\)
• D. \((\sim p \land q) \cap (\sim p \lor p)\)

Hint:

Tautology: statement true for all truth values of its components.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Tautology is always true regardless of truth values.
Step 2: Detailed Explanation:
(A): \(\sim(p \land q) \lor p = (\sim p \lor \sim q) \lor p = T \lor \sim q = T\)
(B): \((p \land q) \rightarrow p = \sim(p \land q) \lor p = T\)
(C): \(q \lor \sim(p \land q) = q \lor (\sim p \lor \sim q) = (q \lor \sim q) \lor \sim p = T\)
(D): \((\sim p \land q) \land (\sim p \lor p) = (\sim p \land q) \land T = \sim p \land q\), which is not always true.
Step 3: Final Answer:
(D) is not a tautology.