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NCERT Class 12- Mathematics: Chapter β 1 Relations and Functions Part 5
Question 24:
For real numbers x and , define if and only if is an irrational number. Then the relation R is
(A) Reflexive
(B) Symmetric
(C) Transitive
(D) None of these
Answer:
(A) Is the correct choice.
Fill in the Blanks in Each of the Examples 25 to 30
Question 25:
Consider the set and R be the smallest equivalence relation on A, then ________
Answer:
.
Question 26:
The domain of the function defined by is ________.
Answer:
Here
Hence the domain of
Question 27:
Consider the set A containing elements. Then, the total number of injective functions from A onto itself is ________.
Answer:
Question 28:
Let Z be the set of integers and R be the relation defined in Z such that if is divisible by . Then R partitions the set Z into ________ pairwise disjoint subsets.
Answer:
Three
Question 29:
Let R be the set of real numbers and be the binary operation defined on R as . Then, the identity element with respect to the binary operation is ________.
Answer:
is the identity element with respect to the binary operation .
State True or False for the statements in each of the Examples 30 to 34.
Question 30:
Consider the set and the relation . R is a transitive relation.
Answer: True.
Question 31:
Let A be a finite set. Then, each injective function from A into itself is not surjective.
Answer: False
Question 32:
For sets A, B and C, let be functions such that is injective. Then both and are injective functions.
Answer: False
Question 33:
For sets A, B and C, let be functions such that is surjective. Then is surjective
Answer: True
Question 34:
Let N be the set of natural numbers. Then, the binary operation in N defined as has identity element.
Answer: False
1.3 EXERCISE
Short Answer (S. A)
Question 1:
Let and the relation R be defined on A as follows:
.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive.
Answer:
Question 2:
Let D be the domain of the real valued function f defined by . Then, write D.
Answer:
Question 3:
Let be defined by and , respectively. Then, find .
Answer: