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

`(p ^^ ~q) ^^ (~p vv q)` is

A

a tautology

B

a contradiction

C

both a tauology and a contradiction

D

neither a tautology nor a contradiction

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Statement - I : (p ^^ ~ q) ^^ (~ p ^^ q) is a fallacy. Statement - II : (p rarr q) harr (~q rarr ~ p) is a tautology.

Observe the following statements I : The dual of [ ~p ^^ q)] vv [ p ^^ {~(q vv ~s)}] is [~(p vv q)] ^^ [p vv{~(q ^^ ~s)}] II : The dual of ~p ^^ [(~q) ^^ (p vv q) ^^ ~r] is ~p vv[~q) vv(p ^^ q) vv ~r] The true statements in the above is/are :

Let p and q be any two propositons Statement 1 : (p rarr q) harr q vv ~p is a tautology Statement 2 : ~(~p ^^ q) ^^ (p vv q) harr p is fallacy

The proposition ~(p vv ~q) vv ~(p vv q) is logically equivalent to

Observe the following statements : Statements - I : (p vv q) ^^ (~p ^^ ~q) is a contradiction. Statement - II : A statement pattern is called a contradiction, it it is a always false, whatever may the truth values of its consitutes statements.

(~q) ^^ p ^^ (p rArr q) is

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

Match the duals of t he statements in List - I : {:(,"List - I",,"List - II"),((1),(p vv q) vv r,(a) ,(p vv q) vv r),((2),(p ^^ q) ^^ r,(b),(p ^^ q) vv (r ^^ s)),((3),(pvv q) ^^ (r vv s),(c ),(p ^^ q) ^^ r):} The correct match is :

AAKASH SERIES-MATHEMATICAL REASONING -Practice Exercise
  1. Let p and q be two proposition given by p : I play cricket during th...

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

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

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

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  5. p rarr q is logically equivalent to

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

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

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

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

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

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  11. Which of the following is always true ?

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  12. Which of the following propositions is a tautology ?

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  13. Which of the following proposition is a tautology ?

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

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

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

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

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

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

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  20. The contrapositive of the following statement, "If the side of a squar...

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