If A and Bare two independent events such that P(A)=1/2 and P(B)=1/5,…

Since A and B are independent events. Therefore,

$P(A ∩  B)= P(A) P(B)=\frac{1}{2}× \frac{1}{5}=\frac{1}{10}$

and, $P(A/B)= P(A)=\frac{1}{2}$

So, alternative (b) is correct.

Now, 

$P(A ∪ B)= P(A) +P(B)-P(A ∩ B)=\frac{1}{2}+\frac{1}{5}-\frac{1}{10}=\frac{3}{5}$

So, alternative (a) is correct.

Now,

$P(A/ A ∪ B)=\frac{P[A ∩(A∪ B)]}{P(A∪ B)}=\frac{P(A)}{P(A∪ B) }=\frac{1/2}{3/5}=\frac{5}{6}$

So, alternative (c) is correct.

and, $P(A ∩B/ \overline{A} ∪ \overline{B})= P(A ∩ B/ (\overline{A ∩ B}))=0$

So, alternatives (d) is not correct.