Mathematical Reasoning
Tautology / Values of r
nta_pyq_2023_jan
Grade 11
Question:
The number of values of $r \in \{p, q, \sim p, \sim q\}$ for which $((p \wedge q) \Rightarrow (r \vee q)) \wedge ((p \wedge r) \Rightarrow q)$ is a tautology, is:
Step-by-Step Solution
Key Concept: Simplify the expression; it reduces to $(\sim p\vee\sim r\vee q)$; check which $r$ values make this always true.
Expression simplifies such that it is tautology when $r=\sim p$ or $r=q$. Number of values $=2$.
Correct Answer: 2