Question

If R ={(a,b): |a-b| is a multiple of 4} is an equivalence relation in the set A=(0,1,2,......9) then find the equivalence class of 1,4 and 5​

Answer 1

SOLVE : (1) R= {(a,b) : (a-b) is a multiple of 4}

• For a= A (a,a) = R / R is reflexive relation: (a-a)=0 which is multiple of 4
• If (a,b) - R [(a,b)] is a multiple of 4 (b,a) - R [(b-a)] is a multiple of 4
• R is symmetric relation.
• If (a,b) - R (a-b) is multiple of 4 and (b,c) - R (b-c) is multiple of 4
• = (a,c) - R (a-c) is multiple of 4