Prove the following bounds on European call options C(S, t), with expiry at time T, on an underlying share price S, with no dividends:

(a) C ≤ S,

(b) C ≥ max(S − Ee^−r(T−t), 0),

(c) 0 ≤ C₁ − C₂ ≤ (E₂ − E₁)e^−r(T−t),

where C₁ and C₂ are calls with exercise prices E₁ and E₂ respectively, and E₁ < E₂.