Mathematical Reasoning
Tautology / Logical Connectives
nta_pyq_2023_jan
Grade 11
Question:
Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $(p \to q)\Delta(p\nabla q)$ is a tautology. Then
\Delta = \wedge, \nabla = \vee
\Delta = \vee, \nabla = \wedge
\Delta = \vee, \nabla = \vee
\Delta = \wedge, \nabla = \wedge
Step-by-Step Solution
Key Concept: Test each of the 4 combinations by constructing truth tables.
Option 3: $(p\to q)\vee(p\vee q)$ is tautology (verified by truth table for all $p,q$ values).
Correct Answer: 3