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Consider the following statements P: S...

Consider the following statements
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

A

` ~ P ^^ ( Q harr ~ R)`

B

` ~ ( Q harr (P ^^ ~ R))`

C

` ~ Q harr ~ P ^^ R)`

D

` ~ ( P ^^ ~ R) harr Q`

Text Solution

Verified by Experts

The correct Answer is:
B
The statement " Suman is brilliant and dishonest iff suman is rich " can be expressed as :
` Q harr ( P ^^ ~ R)`
The negative fo this statement is `~ Q harr (P ^^ ~ R))`
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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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