Can you explain how to do this question step by step?

a) {1,5,6,7,8}

b) {5}

c)  {1,2,4}

d) {} = empty set

Step-by-step explanation:

It is based on set theory.To find "a" first simplify within brackets.A' = everything apart from A which is {5,6,7,8} even universal.B'= everything apart from B which is {1,2,7,8}C'= everything apart from C which is {1,4,5,8}The notation "n" is intersection anything that is common in both.The notation "U" is "Union" everything within both.Rule if Union has more than one common it would still be mentioned.As one won't be written as twice.(B'nC') apart from B and apart from C the common in both is {1,8}A' U {1,8} apart from A  union all in (B'nC')= {1,5,6,7,8}(BnC') same all of B intersection everything apart from C.A'n(BnC') = {5}(B'UC') = everything apart from B and C common in A n(B'UC') ={1,2,4}(AUBUC)' union all ABC but a complement gives 8.(AUBUC) union all ABC but not universal number{1,2,3,4,5,6,7}Intersection between them gives empty set as both are not common.