# NCERT Class 12-Mathematics: Chapter –1 Relations and Functions Part 14

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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**