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Among the following statements, which is...

Among the following statements, which is a tautology ?

A

`p ^^ (p vv q)`

B

`p vv (p ^^ q)`

C

`(p ^^ (p to q)) to q`

D

`q to (p ^^ (p to q))`

Text Solution

Verified by Experts

The correct Answer is:
C
`p ^^ (p vv q)` is F, when `p -= F`
`p vv (p ^^ q)` is F, when `p -= F, q -= F`
and `q to [p ^^ (p to q)]` is F, when `p -= F, q -= T`.
All elements of `[p ^^ (p to q)] to q` are true, so it a tautology.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATHEMATICAL LOGIC -PRACTICE EXERCISE (Exercies 2 (MISCELLANEOUS PROBLEMS))
  1. Which of the following is True?

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

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

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  4. Which of the following is not always true ?

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

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

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

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

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  9. The false statement among the following is

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

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

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

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

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

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

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  16. If S(p,q,r)=(~p)vv(~(q ^^ r)) is a compound statement, then S(~p,~q,~r...

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  17. ~(p vv q)vv (~p ^^ q) is logically equivalent to

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  18. Dual of (x vv y) ^^ (x vv 1) = x vv x ^^ y vv y is

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

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  20. The negation of ~ svv(~ r^^s) is equivalent to :

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