Question

write the smallest equivalence relation on the set {4,5,6}​

Answer 1

Step-by-step explanation:

6,9,2,6

Answer 2

Answer:

The smallest equivalence relation on the set A={4,5,6} is R={(4,4),(5,5),(6,6)}.

As it is reflexive as for all x∈A,(x,x)∈R.

Also this relation R is symmetric as if (x,y)∈R⇒(y,x)∈R for all x,y∈A.

Again this relation is transitive as if (x,y)∈R,(y,z)∈R⇒(x,z)∈R for all x,y,z∈A.

Hence the relation is an equivalance relation.