Mathematical Reasoning
Tautology — Biconditional
nta_pyq_2023_jan
Grade None
Question:
Among the statements: (S1) $((p \vee q) \Rightarrow r) \Leftrightarrow (p \Rightarrow r)$ and (S2) $((p \vee q) \Rightarrow r) \Leftrightarrow ((p \Rightarrow r) \vee (q \Rightarrow r))$
Only (S1) is a tautology
Neither (S1) nor (S2) is a tautology
Only (S2) is a tautology
Both (S1) and (S2) are tautologies
Step-by-Step Solution
Key Concept: Construct truth tables for S1 and S2; S2 has a row where it is false (p=T, q=F, r=F).
S1 is not a tautology (counterexample: p=F,q=T,r=F). S2 is not a tautology (p=T,q=F,r=F). Neither is a tautology.
Correct Answer: 2