Mathematical Reasoning
Tautology Identification
nta_pyq_2023_jan
Grade 11
Question:
Which of the following statements is a tautology?
$p \to (p \wedge (p \to q))$
$(p \wedge q) \to (\sim p \to q)$
$(p \wedge (p \to q)) \to \sim q$
$p \vee (p \wedge q)$
Step-by-Step Solution
Key Concept: Check each option by truth table or algebraic simplification; look for one that is always true.
Option (2): $(p\wedge q)\to(\sim p\to q) = \sim(p\wedge q)\vee(p\vee q) = $ tautology (union of a set and its complement).
Correct Answer: 2