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(p ^^ q) vv ~ p is equivalent to...

`(p ^^ q) vv ~ p` is equivalent to

A

`~p ^^q`

B

`~p vv q`

C

`p ^^ q`

D

`p vv q`

Text Solution

Verified by Experts

The correct Answer is:
B

`(p ^^ q) vv ~ p = ~p vv ( p ^^ q)` [ By commutative law]
`= (~p vv q) ^^ ( ~p vv q)` [ By distributive law]
`= ( p vv ~ p ) ^^ (~ p vv q) `[ By commutative law ]
`= (t ^^ (~ p vvq )` [ By complement law]
`= ~p vv q` [ By identify law]
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