Sets, Relations and Functions Test

Result

Sets, Relations and Functions Test - 30

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Weekly Quiz Competition

Question 1
4 / -1

Given the relation on R = {(a, b), (b, c)} in the set A = {a, b, c} Then the minimum number of ordered pairs which added to R make it an equivalence relation is

A
5

B
6

C
7

D
8

Solution
Question 2
4 / -1

Let R be the relation over the set N × N and is defined by (a,b) R (c,d) ⇒ a + d = b + c Then R is

A
Reflexive only

B
Symmetric only

C
Transitive only

D
An equivalence relation

Solution
Question 3
4 / -1

R = {(x, y) / x, y ϵ I, x² + y² ≤ 4} is a relation in I then domain of R is

A
{0,1,2}

B
{-2,-1,0}

C
{-2,-1,0,1,2}

D
{-2,-1}

Solution
Question 4
4 / -1

An integer m is said to be related to another integer n if m is a multiple of n then the relation is

A
Reflexive and symmetric

B
Reflexive and transitive

C
Symmetric and transitive

D
Equivalence relation
Question 5
4 / -1

If S is defined on R by (x,y) ϵ S ⇔ xy ≥ 0. Then S is......

A
an equivalence relation

B
reflexive only

C
symmetric only

D
transitive only

Solution
Question 6
4 / -1

If A = {1,2,3}, then the number of equivalence relation containing (1,2) is

A
1

B
2

C
3

D
8

Solution
Question 7
4 / -1

For n, m ϵ N n/m means that n is a factor of m, the relation / is

A
reflexive and symmetric

B
transitive and symmetric

C
reflexive transitive and symmetric

D
reflexive transitive and not symmetric
Question 8
4 / -1

Let R be a relation on N defind by R = {(x, y) / x + 2y = 8} The domain of R is

A
{2,4,8}

B
{2,4,6,8}

C
{2,4,6}

D
{1,2,3,4}
Question 9
4 / -1

A real valued function f(x) satisfies the functional equation f(x - y) = f(x) f(y) - f(3 - x) f (3 + y) where f(0) = 1, f(6 - x) is equal to

A
f(x)

B
f(3)

C
f(3) + f(3 - x)

D
-f(x)

Solution
Question 10
4 / -1

If f(2x + 3y, 2x - 3y) = 24xy then f(x, y) is

A
2xy

B
2(x² - y² )

C
x² - y²

D
none of these

Solution