b$)$ The benefits to diversification in holding portfolio $P$ depend critically on ${}_{AB}$; the correlation of returns for A and $B$ :

i$.$ Define what is meant by diversification in the context of $P.$

$[2]$

ii$.$ Discuss whether or not you agree with the above claim.

$[2]$

iii. Provide a mathematical proof to support your argument.

$[4]$