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In the set Z of integers, define m Rn if...

In the set Z of integers, define m Rn if m-n is a multiple of 12. Prove that R is an equivalence relation.

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FULL MARKS-SETS, RELATIONS AND FUNCTIONS-Exercise -1.5
  1. In the set Z of integers, define m Rn if m-n is a multiple of 12. Prov...

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  2. If A= {(x,y) : y = e^(x), x in R } and B = { (x,y) : y = e^(-x), x in ...

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  3. If A = { (x,y) : y = sin x, x in R } and B = { (x,y) : y = cos x, x in...

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  4. The relation R defined on a set A = { 0,-1,1,2} by xRy if |x^(2)+y^(2)...

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  5. If f(x) = |x-2|+|x+2|,x in R, then

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  6. Let RR be the set of all real numbers. Consider the following subsets ...

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  7. Let A and B be subsets of the universal set NN, the set of natural num...

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  8. The number of students who take both the subjects Mathematics and Chem...

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  9. If n[(AxxB)nn(Bxxc)=3,and n(BnnC)=2 then n(A) is ........................

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  10. If n (A) = 2 and n (B cupC) =3 then n [(AxxB) cup (AxxC)] is

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  11. If two sets A and B have 17 elements in common, then the number of ele...

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  12. For non-empty sets A and B, if A sub B "then" (AxxB ) cap (BxxA) is eq...

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  13. The number of relations on a set containing 3 elements is

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  14. Let R be the universal relation on a set X with more than one element....

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  15. Let X = { 1,2,3,4 } and R = { (1,1), (1,2),(1,3),(2,2), (3,3),(2,1),(3...

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  16. The range of the function (1)/(1-2 sinx ) is

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  17. The range of the function f(x) = ||x| -x|,x in RR is

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  18. The rule f(x) = x^(2) is a bijection if the domain and the co-domain a...

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  19. The number of relations form a set containing melements to a set conta...

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  20. The function f : [0,2pi] to 1 [-1,1] defined by f(x) = sin x is

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  21. If the function f : [-3,3] to S defined by f(x) = x^(2) is onto, then ...

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