Let (R, 4-, •) be a ring with a, b, c, d elements of R. State the conditions (from the definition of a ring) that are needed to prove each of the following results.
a) (a + b) + c) = b + (c +a)
b) d + a (b + c) - ab + (d + ac)
c) c{d + b) + ab = (a + c)b + cd
d) a(bc) + (ab)d = (ab)(d + c)