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The negation of (~p ^^ q) vv (p ^^ ~ q) ...

The negation of `(~p ^^ q) vv (p ^^ ~ q)` is

A

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

B

`(p vv ~ q) ^^ (~p vv q)`

C

`(p ^^ ~ q) ^^ (~p vv q)`

D

`(p ^^ ~q)^^ (~q)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `S : (~p ^^ q) vv (p ^^ ~q)`
Then, `~S -= ~[(~p ^^ q) vv (p ^^ ~q)]`
`-= ~ (~p ^^ q) ^^ ~(p ^^ ~q)`
`-= (p vv ~q) ^^ (~p vv q)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATHEMATICAL LOGIC -PRACTICE EXERCISE (Exercies 2 (MISCELLANEOUS PROBLEMS))
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  4. Which among the following is equivalent to r harr s ?

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  5. Which of the following statements is a tautology?

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  6. Which of the following is True?

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  7. If p, q and r are any three logical statements, then which one of the ...

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  8. Among the following statements, which is a tautology ?

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  9. Which of the following is not always true ?

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  10. Converse of the statement ''If a number x is even, then x^(2) is even'...

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  11. If p to (~ p vvq) is false, the truth values of p and q are , respecti...

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  12. The truth values of p,q and r for which (p ^^ q)vv(~r) has truth value...

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  13. p vv ~(p ^^ q) is a

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  14. The false statement among the following is

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  15. Which of the following is true for any two statements p and q ?

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  16. The proposition (p to ~p) ^^ (~p to p) is a

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  17. For integers m and n, both greater than 1, consider the following thre...

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  18. The statement ~(p harr ~q) is

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  19. ~[(~p)^^q] is logocally equivalent to

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  20. The statement p to(q to p) is equivalent to

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