Let S denote set of all integers. Define a relation R on S as 'aR
| Let S denote set of all integers. Define a relation R on S as 'aRb if ab ≥ 0 where a, b ∈ S'. Then R is :
A. Reflexive but neither symmetric nor transitive relation
B. Reflexive, symmetric but not transitive relation
C. An equivalence relation
D. Symmetric but neither reflexive nor transitive relation
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
S = set of all integers
R = { (a, b), a, b S and ab 
0}
For Reflective : aRa => a.a = a2
0
For all integers a, a 
0
For Symmetric: aRb => ab 
0 
a, b 
S
If ab 
0, ba 
0 => bRa
For Transitive:
If ab 
0, bc
0, then also ac 
0
Relation R is reflective, symmetric and transitive.
Therefore, relation is equivalence.
