Let R be an equivalence relation on the set $A= \{1,2,3,4,5\}$ given by R= {(x, y):2 divides (x - y)}. Then equivalence class of 3 is:
Answer & explanation
Correct answer: option 2
$A= \{1,2,3,4,5\}$ R= {(x, y):2 divides (x - y)}
for any $x∈A$
$(x-x)=0$ (divisible by 2)
$⇒(x,x)∈R$ for all $x∈A$ (Reflexive relation)
so for 3 → its equivalence relation is $\{1,3,5\}$
(1-3)(3-3)(5-3) all divisible by 2