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The following statement (p to q) to [(~p...

The following statement `(p to q) to [(~p to q) to q]` is

A

equivalent to ` p to ~ q`

B

a fallocy

C

a tautology

D

equivalent to ` ~ p to q`

Text Solution

Verified by Experts

The correct Answer is:
C
We know that ` p to q = ~ p vv q `
` ~ p to q cong p vv q`
` and , (~ p to q) to q = ( p vv q) to q = ~ ( p vv q) vv q`
` ( ~ p ^^ ~q) vv q = ( ~ p vv q) ^^ ( ~ q vv q)`
` = ( ~ p vv q) ^^ t = ~ p vv q =p to q`
Hence, ` ( p to q ) to [ ( ~p to q) to q]`
` = ( p to q) to (p to q) ` , which is a tautology.
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OBJECTIVE RD SHARMA ENGLISH-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. The contrapositive of p to ( ~ q to ~ r) is

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  2. The contrapositive of the statement "if 2^(2) =5 then I get first cla...

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  3. If x = 5 and y = -2 , then x -2y =9, the contrapositive of this propos...

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  4. The diagonals of a rhombus are perpendicular. The contrapositive of th...

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  5. Which of the following is wrong?

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  6. The symbolic form of logic of the circuit given below is : (RDSMATH...

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  7. Which of the following statements is a tautology ?

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

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  9. Let S be non-empty subset of R. consider the following statement: P:...

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  10. Consider the following statements P: Suman is brilliant Q: Suman i...

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  11. The only statement among the following i.e. a tautology is

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  12. Let p and q be two statements. Amongst the following , the statement t...

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  13. The statement ~(pharr ~q) is

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

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  15. The Bolean Expression ( p ^^ ~ q) vv q vv ( ~ p ^^ q vv ( ~ p ^^ q) ...

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  16. Consider the following two statements: P : If 7 is an odd number, th...

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  17. The negation of A to (A vv ~ B) is

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  18. The following statement (p to q) to [(~p to q) to q] is

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  19. Which of the following is a tautology ?

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  20. The proposition ~p vv( p ^^ ~ q) is equivalent to

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