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