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S is defined in Z by (x,y ) in S hArr |x...

S is defined in Z by `(x,y ) in S hArr |x-y| le 1.` S is ........

A

Reflexive and transitive but not symmetric.

B

Reflexive and symmetric but not transitive.

C

symmetric and transitive but not reflexive.

D

an equivalence relation

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The correct Answer is:
B
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook based MCQs
  1. f(x,y) = (max (x,y))^((min(x,y))) and g(x,y)= max (x,y) - min (x,y) th...

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  2. Let A = {1,2,3}. Then number of equivalence relations containing (1,2)...

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  3. S is defined in Z by (x,y ) in S hArr |x-y| le 1. S is ........

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  4. If S is defined on R by (x,y) inR hArr xy ge 0 . Then S is ...........

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  5. Which of the following defined on Z is not an equivalence relation ?

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  6. If a**b=(ab)/3 on Q^+ then the inverse of a(a ne0) for ** is ......

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  7. The number of binary operation on {1,2,3,......,n} is ..........

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  8. If a**b = a +b on R - {1} , then a^(-1) is ........

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  9. For a**b = a +b + 10 on Z , the identity element is ........

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  10. f:R-{q} rarrR -{1},f(x) = (x-p)/(x-q), p ne q , then f is .........

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  11. Check the injectivity and surjectivity of the following function . f...

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  12. f:[-(pi)/2,pi/2]rarr[-1,1] is a bijection , if ......

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  13. f : R rarr R , f(x) = x^(2) +2x +3 is .......

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  14. If a**b =a^(2) +b^(2) on Z , then ** is ..........

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  15. If a**b = a +b - ab on Q^(+) , then the identity and the inverse of a...

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  16. If a**b=(ab)/3 on Q^(+) , then 3**(1/5**1/2) is .......

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  17. If Delta is defined on P(X) (X ne phi) by , A deltaB = (A cupB) - (A ...

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  18. S is defined on N xxN by ((a,b) , (c,d) in S hArr a +d = b +c ........

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  19. If f:R^(+) rarr R , f(x) = x/(x+1) is .......

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  20. If f : R rarr R , f(x) = [x] , g : R rarr R , g(x) = sinx , h : R rarr...

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