Question

1) Let A = { 1, 2, 3, 4}. Let R be the equivalence relation on A x A defined by (a,b)R(c,d) iff a+d=b+c. Find the equivalence class [(1,3)].

Answer 1

A = { 1, 2, 3, 4}.
R be the equivalence relation on A x A defined by (a,b)R(c,d) iff a+d=b+c

For the set (1,3) we need tofind a and b such that
a +3= b+1
for a=1, on solving we get b =3
for a=2, b = 4
for a= 3 , b= 5 which is not in the set.
So the equivallence class is ,
(1,3), (2,4)