Now I have to construct a portfolio using a European Put option, shares and cash such that the payoff is equal to that of an European call option contract at time 0.
I understand how to do this in relation to put call parity, construct two portfolios; one with a call option and cash and the other with a put option and a share which end up having the same payoff. ie $max(S_T,k)$ and must have identical values today for no arbitrage etc.
The way the question was worded makes it seem like I have to construct a portfolio equal to only the European call option contract ie $max[{S_T-k,0}]$ using a put, shares and cash. Is this possible or would it simply be the first one? the following question states that we should use this portfolio to prove put call parity.
Just subtract $k$ cash from the first two portfolios. As it is an equal subtraction, the fact that the values are equal is retained.