Relation and Function
NCERT Solution
Exercise 1.1 Part 1
Question 1: Determine whether each of the following relations are reflexive, symmetric and transitive.
(i) Relation R in the set A = {1, 2, 3, ..........., 13, 14} defined as
Solution:
Thus, R is not reflexive
Thus, R is not symmetric
Therefore, R is not transitive
Thus, R is neither reflexive nor symmetric and nor transitive.
(ii) Relation of R in the set N of natural numbers defined as
Solution:
Thus, R is not reflexive relation
Thus, R is not symmetric
Thus, R is not transitive.
Therefore, R is neither Reflexive, nor symmetric and nor transitive.
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6}
Solution: Given,R={(x,y):y is divisible by x} in A={1,2,3,4,5,6}
Here, R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3,3), (3, 6), (4,4), 5, 5), (6, 6)}
Thus, R is reflexive.
Thus, R is not symmetric.
Thus, R is transitive.
Therefore, R is reflexive and transitive but not symmetric.
(iv) Relation R in the set Z of all integers defined as
Solution:
In set Z of all integer.
Therefore, R is reflexive relation.
Therefore, R is symmetric.
Therefore, R is transitive.
Thus, R is reflexive, symmetric and transitive.