Give examples of relations the more elegant the better satis

Give examples of relations (the more elegant, the better) satisfying

c) (E2) but not (E1) or (E3)

d) (E3) but not (E1) or (E2)

Solution

If we have a set S = {1,2,3,4,5,6}

and let the subsets of S be :

A = {2}

B = {4,6}

C = {1,3,5}

Now

c) (E2) but not (E1) or (E3)

then the subset of S which is even and prime is = A - (BUC)

d) (E3) but not (E1) or (E2)

then the subset of S which is odd is = C - (AUB)