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The Boolean Expression (p^^~ q)vvqvv(~ p...

The Boolean Expression `(p^^~ q)vvqvv(~ p^^q)` is equivalent to :

A

`~p wedge q`

B

`p wedge q`

C

`p vee q`

D

`p vee ~q`

Text Solution

Verified by Experts

The correct Answer is:
C
Consider, ` (p wedge ~q) vee q vee (~p wedge q)`
`-= [(p wedge ~q) vee q] vee (~q wedge q)`
`-= [( p vee q) wedge (~q vee q )] vee (~p wedge q)`
`-= [(p vee q ) wedge t] vee (~p wedge q)`
` -= (p vee q) vee (~p wedge q)`
`-= (p vee q vee ~ p) wedge (p vee q vee q)`
`-= (q vee t ) wedge (p vee q)`
`-= t wedge (p vee q) -= p vee q`
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