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Let RR be the set of all real numbers. C...

Let `RR` be the set of all real numbers. Consider the following subsets of the plane `RRxxRR`:S = { (x,y) : y=x+1 and 0 `lt x lt 2`} and T = { (x,y) : x-y is an integer }. Then which of the following is true ?

A

"T is an equivalence relation but is not an equivalence relation"

B

"Neither S nor T is an equivalence relation"

C

Both S and T are equivalence relation

D

S is an equivalence relation but T is not an equivalence relation

Text Solution

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The correct Answer is:
A
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PREMIERS PUBLISHERS-SETS,RELATIONS AND FUNCATIONS-SOLUTION TO EXERCISE 1.5
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  2. If f(x) = |x-2|+|x+2|,x in R, then

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

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

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

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  6. If n ((AxxB) cap (AxxC)) = 8 "and" n (B cup C) =2, then n (A) is

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

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

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

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

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

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

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

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

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  16. The number of relations from a set containi 4 elements to a set contai...

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

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

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  19. Let X = { 1,2,3,4}, Y = {a,b,c,d} and f={(1,a), (4,b), (2,c),(3,d),(2,...

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  20. The inverse of f(x) = {(x,if,xlt1),(x^(2),if,1lt=xlt=4"is"),(8sqrt(x),...

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