Page 11 - Mathematics Class - XII

Viva-Voce

1. What is relation?
Ans. Relation in a set A is a subset of A × A. Or
A connection between the elements of two or more sets is relation. The sets must be non-empty.

2. What is empty relation? Give an example.
Ans. If no element of set A is related to any element of A, then the relation R in A is an empty relation, i.e.
R = φ.
For example, set A consists of only 100 hens in a poultry farm. Is there any possibility of finding a relation
R of getting any elephant in the farm? No! R is a void or empty relation since there are only 100 hens and
no elephant.
3. When is the relation transitive?
Ans. A relation in a set A is transitive if, (a, b) ∈ R, (b, c) ∈ R, then (a, c) ∈ R, for all a, b, c ∈ A.

4. What is universal relation?
Ans. A relation R in a set, say A is a universal relation if each element of A is related to every element of A,
i.e., R = A × A.

5. How many relations can be established from set A having n elements to set B having m elements?
Ans. Number of relations from set A having n elements to set B having m elements is 2 .
mn

MCQs

1. Let A = {a, b, c, d} and B = {1, 4, 9} then number of relation from A to B will be
a) 12 b) 1024 c) 256 d) 4096
2. Let R = {(1, 1), (1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}, then relation R in the set A = {1, 2, 3, 4} is
a) Transitive b) Asymmetric c) Reflexive d) None of these
3. For real numbers x and y, R is defined as if and only if x – y + 5 is an irrational number, then relation R
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will be
a) Reflexive b) Symmetric c) Transitive d) None of these
4. An integer m is related to other integer n such that m is factor of n. Which of the relation between m and n.
a) Reflexive and transitive b) Symmetric and transitive
c) Equivalence relation d) Reflexive and symmetric

5. If R = {(a, b) : a is brother of b; a, b ∈ A} is defined on set A where A is the non-empty set children in the
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family. Then R
a) Transitive but not symmetric b) Symmetric but not transitive

c) Neither symmetric nor transitive d) Equivalence relation
6. Let a relation R in set R defined as a R b if a ≥ b, then relation R
a) Symmetric and transitive but not reflexive b) An equivalence relation
c) Reflexive and transitive but not symmetric d) Symmetric but neither transitive nor reflexive

Answers: 1. d) 4096 2. b) Asymmetric 3. c) Transitive 4. a) Reflexive and transitive
5. a) Transitive but not symmetric 6. c) Reflexive and transitive but not symmetric

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