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The contrapositive of the statement, 'If...

The contrapositive of the statement, 'If x is a prime number and x divides ab then x divides a or x divides b", can be symnolically represented using logical connectives, on appropriately defined statements p, q, r, s as

A

`(~r vv ~s) rarr (~p ^^ ~q)`

B

`(r ^^ s) rarr (~p ^^ ~q)`

C

`(~r ^^ ~s) rarr (~p vv ~q)`

D

`(r vv s) rarr (~p vv ~q)`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-MATHEMATICAL REASONING -Practice Exercise
  1. The contrapositive of the statement, 'If x is a prime number and x div...

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  2. Which of the following is a proposition

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  3. Let p and q be two proposition given by p : I play cricket during th...

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  4. If x = 5 and y = -2, then x - 2y = 9. The contrapositive of this propo...

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  5. Consider the proposition : "If we control population growth, then we p...

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  6. Consider the following propositions p : I have the raincoat. q : I...

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  7. p rarr q is logically equivalent to

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  8. The contrapositive of p rarr (~q rarr ~r) is

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  9. The negation of p ^^ ~(q ^^ r) is

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  10. The contra positive of (~p ^^ q) rarr ~r is

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  11. Which of the following is logically equivalent to (p ^^ q) ?

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  12. (p ^^ ~q) ^^ (~p vv q) is

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  13. Which of the following is always true ?

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  14. Which of the following propositions is a tautology ?

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  15. Which of the following proposition is a tautology ?

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  16. Observe the following statements I : The dual of [ ~p ^^ q)] vv [ p...

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  17. Match the duals of t he statements in List - I : {:(,"List - I",,"Li...

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  18. Match the duals of the statements in list - I : {:(,"List - I",,"Lis...

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  19. Observe the following statements : Statements - I : (p vv q) ^^ (~p ...

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  20. Observe the following statements Statement - I : p vv ~(p ^^ q) is a...

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  21. Consider the following two statements P :if 7 is an odd number, then...

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