Mathematical Reasoning
Tautology
nta_pyq_2023_jan
Grade None
Question:
The statement $(p \wedge (\sim q)) \Rightarrow (p \Rightarrow (\sim q))$ is
equivalent to $(\sim p) \vee (\sim q)$
a tautology
equivalent to $p \vee q$
a contradiction
Step-by-Step Solution
Key Concept: Simplify: antecedent $p\wedge\sim q$ implies consequent $p\Rightarrow\sim q = \sim p\vee\sim q$; show it is always true.
$(p\wedge\sim q)\Rightarrow(\sim p\vee\sim q) \equiv \sim(p\wedge\sim q)\vee(\sim p\vee\sim q) \equiv (\sim p\vee q)\vee(\sim p\vee\sim q) \equiv \sim p\vee t \equiv t$. It is a tautology.
Correct Answer: 2