Relations And Functions Test

Result

Relations And Functions Test - 2

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Question 1
1 / -0

A and B are two sets having 3 and 4 elements respectively and having 2 elements in common. The number of relations, which can be defined from A to B, is

A
2⁵

B
2¹⁰ – 1

C
2⁷

D
None of these

Solution

The number of elements in A × B is 12.Hence the number of subsets of A × B is 2¹², which includes the empty set.
Question 2
1 / -0

The number of relations that can be defined on set A = {a, b, c, d} is

A
24

B
16

C
4⁴

D
2¹⁶

Solution

The number of relations on A is 2⁴ = 2¹⁶.
Question 3
1 / -0

Which of the following relations is a function?

A
R = {(x, y) : x² + y² ≤ 9} on R

B
A = {1, 2, 3}, B = {1, 2, 3, 4, 5} and R = {(x, y) : 5x + 2y} is a prime number on A .

C
A = {(1, 2, 3}, B = {1, 2, 3, 4, 5, 6, 7} and R = {(x, y) | y =x² – 3x + 3} on A

D
None of these

Solution

All the given functions do not satisfy the function property, i.e. every input has a unique output.