Relation and Function
NCERT Exemplar Problem
Long Answer Type Part 1
Question 16: If A = {1, 2, 3, 4}, define relations on A which have properties of being
(a) Reflexive, transitive but not symmetric
Solution:
(b) Symmetric but neither reflexive nor transitive
Solution:
(c) Reflexive, symmetric and transitive.
Solution:
Question: 17 – Let R be relation defined on the set of natural number N as follows:
Find the domain and range of the relation R. Also, verify whether R is reflexive, symmetric and transitive.
Solution:
Thus, R is neither reflexive, nor symmetric and nor transitive.
Question – 18 – Given A {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:
(a) an injective mapping from A to B
Solution:
But this is an injective mapping.
(b) a mapping from A to B which is not injective
Solution:
Here it is clear that it is not an injective mapping.
(c) a mapping from B to A
Solution:
Here it is clear that every first component is from B and second component is from A, thus h is a mapping from B to A.
Question – 19: Give an example
(i) Which is one-one but not onto
Solution:
Let A be the set of all 100 students in a school in a particular class say ninth.
be the mapping defined by
Here it is clear that f is one-one because no two students of the same class can have the same roll number.
Let roll number of student start from 1 and ends on 100.
This implies that 101 in N is not the roll number of any of the student of the class, so that 101 is not an image of any element of A under f.
Therefore, f is not onto.
(ii) Which is not one-one but onto
Solution:
This is onto but not one-one.
(iii) Which is neither one-one nor onto
Solution:
Here it is neither one-one nor onto.