Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (e) Is the subset Y = {a, c, d} of X closed under ? Explain. Solution Let X = {a,b,c,d} and let be the binary operation on X given by the following table: a b c d a d c a b b c b a c c a a d c d b d c a (e) Is the subset Y = {a, c, d} of X closed under ? Explain. if x, y Y then x y Y then it is closed as Y subset of X as Y = {a,c,d} x,y can only be a,c,d so we check a*c = a c*a = a a*d = b d*a = b c*d = c d*c = c as we can see there is extra element b so it is not closed .