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+14 votes
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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 $p \vee q$

  4. a contradiction

  5. none of the above

asked in Mathematical Logic by Veteran (59.7k points)
edited by | 873 views

4 Answers

+11 votes
Best answer

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

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

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

$\equiv (p \wedge q)$


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

answered by Boss (40.7k points)
edited by
+13 votes
OPTION (B)
answered by Active (2.6k points)
+11 votes
p ^ (~p v q)

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

= False V (p^q)

= (p^q)
answered by (277 points)
+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 )
answered by Boss (20.9k points)

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