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The false statement among the following ...

The false statement among the following is

A

`p ^^ (~ p)` is a tautology

B

`(p to q) harr (~q to ~ p)` is a conbtradiction

C

`~(~p)harr p` is a tautology

D

`p vv (~p)` is tautology

Text Solution

Verified by Experts

The correct Answer is:
B
`p to q` is equivalent to `~ q to ~ p`.
`therefore (p to q) harr (~ q to ~p)` is a tautology but not a contradiction.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATHEMATICAL LOGIC -PRACTICE EXERCISE (Exercies 2 (MISCELLANEOUS PROBLEMS))
  1. If p, q and r are any three logical statements, then which one of the ...

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

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  3. Which of the following is not always true ?

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

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

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

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

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  8. The false statement among the following is

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

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

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

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

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

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

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

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

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

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

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

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  20. Given statement is 'if x = y, then x^(2) = y^(2), and the statement ar...

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