# NCERT Class 12-Mathematics: Chapter – 1 Relations and Functions Part 14 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 49**:

Let the relation R be defined on the set . Then R is given by ________.

**Answer**:

**Question 50**:

Let . Then ________ and ________.

**Answer**:

**Question 51**:

Let be defined by Then ________

**Answer**:

**Question 52**:

If , then ________.

**Answer**:

## State True or False for the Statements in Each of the Exercises 53 to 63

**Question 53**:

Let be a relation defined on the set . Then R is symmetric, transitive but not reflexive.

**Answer: False**

**Question 54**:

Let be the function defined by . Then is invertible.

**Answer: False**

**Question 55**:

Every relation which is symmetric and transitive is also reflexive.

**Answer: False**

**Question 56**:

An integer is said to be related to another integer if is integral multiple of . This relation in Z is reflexive, symmetric and transitive.

**Answer: False**

**Question 57**:

Let and N be the set of natural numbers. Then the mapping A defined by , is onto.

**Answer: True**

**Question 58**:

The relation R on the set defined as is reflexive, symmetric, and transitive.

**Answer: False**

**Question 59**:

The composition of functions is commutative.

**Answer: False**

**Question 60**:

The composition of functions is associative.

**Answer: True**

**Question 61**:

Every function is invertible.

**Answer: False**

**Question 62**:

A binary operation on a set has always the identity element.

**Answer: False**