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Let R1 and R2 be equivalence relations o...

Let `R_1` and `R_2` be equivalence relations on a set A, then `R_1uuR_2` may or may not be

A

S is reflexive but not symmetric

B

S is reflexive and symmetric but not transitive

C

S is an equivalence relation

D

S may not be transitive

Text Solution

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-SETS, RELATIONS AND FUNCTIONS-EXERCISE (CONCEPT -BASED (SINGLE CORRECT ANSWER TYPE QUESTIONS) )
  1. Let ~ be a relation defined on N xx N as follows: (a,b),(c,d) in N ...

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  2. Let A = {a, b, c} andR = {(a, b), (b, c)}. The minimum number of order...

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  3. Suppose A and B have exactly n elements in common, then the number of ...

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  4. On Z, define R as follows: a, b in Z, aRb if 7|(a^(2) -b^(2)), then ...

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  5. Suppose R is a reflexive and transitive relation on a set A and let S ...

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  6. Let R1 and R2 be equivalence relations on a set A, then R1uuR2 may or ...

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  7. On Z, define R as follows: a,b in Z, aRb if 3|(a^(2) - b^(2)), then ...

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  8. Let f(x) = sin(pi[x]) + sin([pi^(2)]x) + cos ([-pi^(2)]x/3) AA x in R,...

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  9. The domain of f(x)="log"|logx|i s (0,oo) (b) (1,oo) (c) (0,1)uu(1,oo...

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  10. Let /be a function such that 3f(x) + 22f(1/x) = 7x, AA x ne 0, then...

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  11. Let f: R to R be defined by f(x) = 5^(2x)/(5^(2x) + 5), then f(x) + ...

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  12. Let g(x)=1+x-[x] and f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0)...

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  13. If f (x) = 27x^(3) -(1)/(x^(3)) and alpha, beta are roots of 3x - (1)/...

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  14. Let f(x) = ln(x-1)(x-3) and g(x) = ln(x-1) + ln(x-3) then,

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  15. Let f(x) = cos(x) + cos(sqrt(3)x) AA x in R. The number of values of x...

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  16. The domain of f(x) = sqrt((2-|x|)/(3-|x|)) is

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  17. The range of f(x) = sqrt(3x^(2) - 10 x + 12) is

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  18. The domain of f(x) = cos^(-1) {log(2) (1/2x^(2))} is

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  19. Suppose f: R to R be defined by f(x) ={{:(x, if x in Q),(1-x, if x i...

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  20. Let f:[4,infty) to [1,infty) be defined by f(x) = 11^(x(4-x)) AA x ...

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