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The negation of the propostion " if a qu...

The negation of the propostion " if a quadrillatcral is a square, then it is a rhombus" is

A

if a quadrilateral is not a square, then it is a rhombus

B

if a quadrillateral is a square, then it is not a rhombus

C

a quadrillateral is a square and it is not a rhombus

D

a quadrillateral is not a square and it is a rhombus.

Text Solution

Verified by Experts

The correct Answer is:
C
Let p and q be the propositions as given below :
p : A quadrilateral is a square
q : A quadrilateral is a rhombus
The given proposition is ` p to q `
Now ,` (p to q) cong p ^^ ~ q`
Therefore, the negation of the given proposition is : A quadrilateral is a square and it is not a rhombus.
The given proposition is `p to q`
Now, ` ~ ( p to q ) cong p ^^ ~ q`
Therefore, the negation of the given proposotion is :
A quadrilateral is a square and it is not a rhombus.
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OBJECTIVE RD SHARMA-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. Which of the following is always true ?

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  2. Negation of the statement ~ p to (q vv r) is

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  3. The negation of the propostion " if a quadrillatcral is a square, then...

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  4. The contrapositive of (pvvq) to r is

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  5. The contrapositive of p to ( ~ q to ~ r) is

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

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

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

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  9. Which of the following is wrong?

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

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  11. Which of the following statements is a tautology ?

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

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

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

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

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

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

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

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

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  20. Consider the following statements. p : if 7 is an odd number , then ...

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