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11th Standard English Medium Maths Subject Sets, Relations and Functions Creative 2 Mark Questions with Solution Part - I

Published on: 24/06/2021

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Std: 11th Standard - Maths

chapter: - Creative Questions

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Questions:

Generic 2

5 x 2 = 10

Let A be the set consisting of children and elders of a family. Let R be the relation defined by aRb if a is a sister of b.

Let C be the set of all circles in a plane and define a circle C is related to a circle C', if the radius of C is equal to the radius of C'

Using Venn diagram verify (AUB)'=A'⋂B'

If U = {x : 1 ≤ x ≤ 10, x ∈ N}, A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 9, 10} then find A'UB'.

If A = {x : x is a multiple of 5, x ≤ 30 and x ∈ N}
B = {1, 3, 7, 10, 12, 15, 18, 25} then find A⋂B

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Answers Key:

Generic 2

5 x 2 = 10

This relation is to be looked into carefully. A woman is not a sister of herself. So it is not reflexive. It is not symmetric also. Clearly it is not transitive. So it is not an equivalence relation. (If we consider the same relation on a set consisting only of females, then it becomes symmetric, even in this case it is not transitive).

In this example, it is easy to see that whenever a circle C₁ is related to C₂ then C₂ is also related to C₁. Hence the relation is symmetric, whereas in example 1 it does not hold as whenever 2 divides 4 then it does not imply 4 divides 2 as 4 does not divide 2.

From (ii) and (v), (AUB)' = A' ∩ B'

Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 3, 5, 7, 9}
B = {2, 3, 5, 9, 10}
A' = {2, 4, 6, 8, 10}
B' = {1, 4, 6, 7, 8}
A'UB' = {1, 2, 4, 6, 7, 8, 10}

Given A = {5, 10, 15, 20, 25, 30}
B = {1, 3, 7, 10, 12, 15, 18, 25}
Now A⋂B = {10,15, 25}