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If S is defined on R by (x,y) inR hArr x...

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

A

an equivalence relation

B

reflexive only

C

symmetric only

D

transitive only

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The correct Answer is:
A
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook based MCQs
  1. Let A = {1,2,3}. Then number of equivalence relations containing (1,2)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. f: R rarr R , f(x) ={{:(-1,xlt0,),(0,x=0 , g:R rarr R ","g(x)=),(1,xgt...

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