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Let `Z` be the set of all integers and `Z_0` be the set of all non-zero integers. Let a relation `R` on `ZxxZ_0` be defined as follows: `(a ,\ b)\ R\ (c ,\ d)hArra d=b c` for all `(a ,\ b),\ (c ,\ d) in ZxxZ_0` Prove that `R` is an equivalence relation on `ZxxZ_0`

A

Reflexive only

B

Symmetric only

C

Transitive only

D

Equivalence

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The correct Answer is:
D
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AAKASH INSTITUTE ENGLISH-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. Let S be the set of all real numbers. Then the relation R= {(a,b):1+...

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  2. Let w denotes the set of words in the English dictionary. Define the r...

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  3. Let Z be the set of all integers and Z0 be the set of all non-zero int...

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  4. For real numbers x and y , define x\ R\ y iff x-y+sqrt(2) is an irrati...

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  5. If f(1)(x) = 2x + 3, f(2)(x) = 3x^(2) + 5, f(3)(x) = x + cos x are def...

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  6. Which of the functions defined below is one one function ?

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  7. Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0, where a, b, c, d in R. If...

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  8. Let A = {1, 2, 3}, B = {a, b, c}, C {a(1), b(1), c(1), d(1), e(1)} an...

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  9. Select the correct match

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  10. Let f : [2, 4) rarr [1, 3) be a function defined by f(x) = x - [(x)/(2...

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  11. Identify the correct option

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  12. Which of the following function is an even function ?

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  13. A function f(x) given by f(x)={{:(x^(2)sin""(pix)/(2), |x| lt1),(x|...

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  14. Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0. Then f(x)...

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  15. Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R a...

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  16. Let f: R rarr R be a function defined as f(x)=[(x+1)^2]^(1/3)+[(x-1)^2...

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  17. Let f(x) = |sinx| + |cosx|, g(x) = cos(cosx) + cos(sinx) ,h(x)={-x/2...

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  18. Identify the incorrect statement

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  19. Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation fo...

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  20. Let f(x) = tan x, x in (-pi/2,pi/2)and g(x) = sqrt(1-x^2) then g(f(x)...

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