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Let p, q and r be three logical statemen...

Let p, q and r be three logical statements. Which of the following-is true?

A

~ `(p vv ~ q ) equiv ~ p vv q`

B

`~ ( p vv q) ^^ ( ~ r) equiv (~p) vee (~q) vee (~r)`

C

`~ (~ p vee ~q) equiv p ^^ q `

D

`~ [ p ^^ (~ q) ] equiv p vee q `

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If p, q and r are any three logical statements, then which one of the following is correct ?

    A
    `~[p ^^ (~q)]-=(~p)^^ q`
    B
    `~(p vv q)^^(~ r)-=(~p)vv (~q)vv(~r)`
    C
    `~[p vv(~q)]-=(~p)^^ q`
    D
    `~[p ^^ (~q)]-=(~p)^^ ~q`

  • p:57 is an odd prime number. q:8 is divisor of 24. r:12 is L.C.M of 5 and 3 are three logical statements, then which one of the following is false?

    A
    `pvv(~q^^r)`
    B
    `~pvv(q^^r)`
    C
    `(p^^)v~r`
    D
    `(pvvq)^^~r`

  • If p, q are true and r is false statement then which of the following is true statement?

    A
    `(p ^^q) vv ` r is F
    B
    `(p ^^ q) ^^ r` is T
    C
    `(p vv q) ^^ (p vv r) ` is T
    D
    `( p ^^ q) vv ( p ^^ r) `is F

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