Mathematical Reasoning
Truth Values / Making Implication False
nta_pyq_2023_jan
Grade 11
Question:
If $p$, $q$ and $r$ are three propositions, then which of the following combination of truth values of $p$, $q$ and $r$ makes the logical expression $\{(p \vee q) \wedge ((\sim p) \vee r)\} \to ((\sim q) \vee r)$ false?
$p = T, q = F, r = T$
$p = T, q = T, r = F$
$p = F, q = T, r = F$
$p = T, q = F, r = F$
Step-by-Step Solution
Key Concept: An implication is false only when antecedent is true and consequent is false; check each option.
For option (3): $p=F,q=T,r=F$: antecedent $(F\vee T)\wedge(T\vee F)=T$; consequent $F\vee F=F$. Implication is False.
Correct Answer: 3