TD - Simple bounds on European call options

QUESTION
Prove the following simple bounds on European call options on an asset that
pays no dividends:
(a) C ≤ S
(b) C ≥ S − k exp(−r[T − t])
(c) If two otherwise identical calls have exercise prices K1 and K2 with
K1 < K2, then
0 ≤ C(S,t, K1) − C(S,t, k2) ≤ k2 − k1.
(d) If two otherwise identical call options have expiry times T1 and T2 and
T1 < T2 then
C(S,t, T1) ≤ C(S,t, T2).