Question
Mathematics Question on Relations and functions
Which of the following are not equivalence relations on I?
A
aRb if a + b is an even integer
B
aRb if a - b is an even integer
C
aRb if a < b
D
aRb if a = b
Answer
aRb if a < b
Explanation
Solution
The relations given in OPTIONS (1), (2) and (4) are clearly reflexive, symmetric and transitive. On the other hand, the relation of OPTION (C) IS transitive but neither reflexive nor symmetric.