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