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The proposition (~p)vv(p^~q) is equival...

The proposition `(~p)vv(p^~q)` 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 p) ^^ (~p vv q)` [by distributive law]
`-= (p vv ~ p) ^^ (~p vv q)` [by commutative law]
`-= T ^^ (~ p vv q)` [ by complement law]
`-= ~ p vv q` [by identity law]
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