( p q) (q r) is a - Vidyadip

MCQ

$(\sim p \wedge \sim q) \wedge(q \wedge r)$ is a

A
tautology
B
contingency
✓
contradiction
D
neither tautology nor contradiction

✓

Answer

Correct option: C.

contradiction

(C)
$(\sim p \wedge \sim q) \wedge(q \wedge r)$
$\equiv \sim p \wedge(\sim q \wedge q) \wedge r \quad \ldots[$ Associative Law $]$
$\equiv \sim p \wedge F \wedge r \quad \ldots[$ Complement Law $]$
$\equiv F \quad \ldots[$ Indentity Law $]$
∴ Given statement is contradiction.

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