Question

a) Find the smallest equivalence relation A={2, 5 ,7 }​

Answer 1

The smallest equivalence relation of A={2,5,7} is

A={x:x=(2a+1),a belongs to natural number,a<4}

Answer 2

Step-by-step explanation:

A = { 2, 5, 7 }

R = { ( 2,2 ), ( 5,5 ), ( 7,7 ), ( 2,5 ), ( 2,7 ), ( 5,2 ), ( 7,2 ) }

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

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

Hence the relation is an equivalance relation.