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For any two statements p and q, the nega...

For any two statements p and q, the negation of the expression `p vee (~p wedge q)` is

A

`~ p wedge ~q`

B

`~p vee ~q`

C

`p wedge q`

D

`p harr q`

Text Solution

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The correct Answer is:
A
` because p vee ((~p) wedge q)`
` =(p vee (~p)) wedge (p vee q) " " `[by Distributive law]
`=p vee q " " [ because p vee (~p) " is tautology"]`
So negation of `p vee ((~p) wedge q)`
`= ~[p vee (~p) wedge q]= ~ (p vee q)`
`=(~p) wedge (~q) " " ` [by Demorgan's law]
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