Question

Define sets U, A, B, and C as shown below. Find A'n (BUC').

U= ({a,b,c,d,e,f.g.h}
A = {f,g,h}
B={a,g,h}
C={a,b,c,d,e)

Answer 1

{a}

Explanation:

You want the set A'∩(B∪C') given the definitions of each of the sets U, A, B, C.

Inverse sets

The inverse of a set is the set of elements of the universal set that are NOT in the given set.

A' = {a, b, c, d, e, f, g, h} - {f, g, h} = {a, b, c, d, e}

C' = {a, b, c, d, e, f, g, h} - {a, b, c, d, e} = {f, g, h}

Union

The union of two sets is the list of elements in either of the two sets.

B∪C' = {a, g, h} +{f, g, h} = {a, f, g, h}

Intersection

The intersection of two sets is the list of elements common to both:

A'∩(B∪C') = {a, b, c, d, e} ∩ {a, f, g, h} = {a}