The elasticity $$ of an option price $V$ is the ratio of the relative change in $V$ to small relative changes

in $S.$ More precisely:

$$:$=\underset{S0}{lim}\frac{\frac{(V(S+S,t)-V(S,t))}{V(S,t)}}{\frac{S}{S}}$

Show that

$($a$)=(\frac{S}{V(S,t)})$;

$($b$)1$ for a European call option, and give a financial interpretation;

$($c$)0$ for a European put option, and give a financial interpretation.