Question

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

Answer 1

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.