Question

Let a = {2, 9}, b = {9, 13, 28}, d = {40} and s = sample space = a ∪ b ∪ d. identify bc ∪ a.

Answer 1

Presumably you want to find $B^C\cup A$, where $B^C$ presumably denotes the complement of $B$. We have

$S=A\cup B\cup D=\{2,9,13,28,40\}$

and since $B=\{9,13,28\}$, we have $B^C$ the set of all values in $S$ *not* in $B$; that is, $B^C=\{2,40\}$.

Now

$B^C\cup A=\{2,40\}\cup\{2,9\}=\{2,9,40\}$