Mathematical Reasoning
Tautology and Contradiction
nta_pyq_2023_jan
Grade 11
Question:
(S1) $(p \Rightarrow q) \vee (p \wedge (\sim q))$ is a tautology. (S2) $((\sim p) \Rightarrow (\sim q)) \wedge ((\sim p) \vee q)$ is a Contradiction. Then
only (S2) is correct
both (S1) and (S2) are correct
both (S1) and (S2) are wrong
only (S1) is correct
Step-by-Step Solution
Key Concept: Check S1: $(p\Rightarrow q)\vee(p\wedge\sim q)=(\sim p\vee q)\vee(p\wedge\sim q)$. Check S2 by truth table.
S1 is a tautology (always true). S2 truth table shows it is not always false (not a contradiction). Only S1 is correct.
Correct Answer: 4