TD - a European vanilla call, the delta of an option and the portfolio

Question
In this question YOU MAY ASSUME that the value V of a European Vanilla
Call is given by
V − SN(d1) − Ee
−r(T −t)N(d2)
where
d1 =
log(S/E) +
³
r +
1
2
σ
2
´
(T − t)
σ
√
T − t
,
d2 =
log(S/E) +
³
r −
1
2
σ
2
´
(T − t)
σ
√
T − t
,
N(p) =
1
√
2π
Z p
−∞
e
−q
2/2
dq
and S, E, t, T, σ and r denote respectively the asset price, the strike price,
the time, the expiry, the volatility and the interest rate.
(a) Show that
∂
∂S
(N(d1)) =
1
q
2π(T − t)
e
−d
2
1
/2
σS
and calculate
∂
∂S
(N(d2)).
Hence show that the DELTA, defined by ∆c = ∂V/∂S for a European
Vanilla Call is given by
∆c = N(d1).
What does the delta of an option measure?
Denote the value of a call by C and the value of a put by P. By
considering a portfolio which is long one asset, long one put and short
on call, show that
C − P = S − Ee
−r(T −t)
and hence show that the delta ∆p for a European Vanilla Put is
∆p = N(d1) − 1.
Give a financial reason why ∆p < ∆c.