Set Theory And Relations Test

Result

Set Theory And Relations Test - 1

Score
-
out of -
Rank
-
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TIME Taken - -

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Question 1
1 / -0

Given two finite sets A and B such that n(A) = 2, n(B) = 3. Then total number of relations from A to B is

A
4

B
8

C
64

D
None of these

Solution

Here n(A × B) = 2 × 3 = 6

Since every subset of A × B defines a relation from A to B, number of relation from A to B is equal to number of subsets of A × B = 26 = 64, which is given in (c).
Question 2
1 / -0

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then R^-1 is given by

A
{(2, 1), (4, 2), (6, 3).....}

B
{(1, 2), (2, 4), (3, 6)....}

C
R^-1is not defined

D
None of these

Solution

R = {(2, 1), (4, 2), (6, 3),......} So, R^-1 = {(1, 2), (2, 4), (3, 6),.....}.
Question 3
1 / -0

The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

A
Reflexive but not symmetric

B
Reflexive but not transitive

C
Symmetric and Transitive

D
Neither symmetric nor transitive

Solution

Since (1, 1); (2, 2); (3, 3) ∈ R therefore R is reflexive. (1, 2) ∈ R but (2, 1) ∉ R, therefore R is not symmetric. It can be easily seen that R is transitive.