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The proposition $p \wedge (\sim p \vee q)$ is:

1. a tautology

2. logically equivalent to $p \wedge q$

3. logically equivalent to $p \vee q$

5. none of the above

edited | 803 views

$p \wedge (\sim p \vee q)$

$\equiv (p \wedge \sim p) \vee (p \wedge q)$

$\equiv F \vee (p \wedge q)$

$\equiv (p \wedge q)$

Hence, Option(B) logically equivalent to $(p \wedge q)$.

edited by
OPTION (B)
p ^ (~p v q)

= (p ^ ~p) v (p ^ q)

= False V (p^q)

= (p^q)
+1 vote
P ∧ ( ∼P ∨ Q )  ≡  ( P ∧ ~P ) ∨ ( P ∧ Q )

≡ ( F ) ∨ ( P ∧ Q )    { (P ∧ ~P) is always False and (P ∨ ~P) is always True }

≡ ( P ∧ Q )