NCERT Solutions Class 12 Mathematics Chapter 1: Number System Exercise 1.1

Concept Chapter 1 Class 12 Maths RELATIONS AND FUNCTIONS Ncert Solutions

Relation
Types of Relation
Reflexive Relation

Symmetric Relation

Transitive Relation
Equivalence Relation

Functions
Types of Function
One to One Function
Many to one Function

Many one onto Function
One One onto Function(Injective)

Exercise 1.1 Chapter 1 Class 12 Maths RELATIONS AND FUNCTIONS Ncert Solutions

Q1. Determine whether each of the following relations are reflexive, symmetric and transitive:
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y) : y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y) : y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y) : x – y is an integer}

Q 1. Determine whether each of the following relations are reflexive, symmetric and transitive:
(i) Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as
R = {(x, y) : 3x – y = 0}

Q 1.Determine whether each of the following relations are reflexive, symmetric and transitive:
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y) : x and y work at the same place}
(b) R = {(x, y) : x and y live in the same locality}
(c) R = {(x, y) : x is exactly 7 cm taller than y}
(d) R = {(x, y) : x is wife of y}
(e) R = {(x, y) : x is father of y}

2. Show that the relation R in the set R of real numbers, defined as
R = {(a, b) : a ? b2} is neither reflexive nor symmetric nor transitive.

3. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

4. Show that the relation R in R defined as R = {(a, b) : a ? b}, is reflexive and transitive but not symmetric.

5. Check whether the relation R in R defined by R = {(a, b) : a ? b3} is reflexive, symmetric or transitive.

6. Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

7. Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.

8. Show that the relation R in the set A = {1, 2, 3, 4, 5} given by
R = {(a, b) : |a – b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.

9. Show that each of the relation R in the set A = {x ? Z : 0 ? x ? 12}, given by
(i) R = {(a, b) : |a – b| is a multiple of 4}
(ii) R = {(a, b) : a = b}