The proposition p ^ (~p v q) is:
A. a tautology
B. logically equivalent to p ^ q
C. logically equivalent to p ^ ~q
D. a ...

Question

The proposition p ^ (~p v q) is:
A. a tautology
B. logically equivalent to p ^ q
C. logically equivalent to p ^ ~q
D. a contradiction
E. none of the above

Accepted Answer

p ^ (~p v q) is logically equivalent to p ^ q Apply the distributive law to simplify p ^ (~p v q). Distributing p over the disjunction gives (p ^ ~p) v (p ^ q). Since p ^ ~p is always False, the whole expression reduces to p ^ q. So the proposition is logically equivalent to p ^ q.

The proposition p ^ (~p v q) is: A. a tautology B. logically equivalent to p ^ q C. logically equivalent to p ^ ~q D. a contradiction E. none of the above