Question 191247
If U = {All letters of the alphabet}, A = {c, d, e, f} and B = {e, f, g, h, k}, then


A' = {a, b, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}


and 


B' = {a, b, c, d, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}


A': set with members that are in U but not in A


B': set with members that are in U but not in B


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a) Combine sets A & B (take out duplicates)

A U B = {c, d, e, f, g, h, k}


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b) Find common elements in sets A & B

A ∩ B = {e, f}


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c) Find common elements in sets A' & B'

A′ ∩ B′ = {a, b, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}



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(d) Combine sets A' & B' (take out duplicates)


A′ U B′ = {a, b, c, d, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}


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(e)  Combine sets A & B'

A U B′ = {a, b, c, d, e, f, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}



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(f) Hint: use part e)

(A U B′) ∩ B = {a, b, c, d, e, f, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z} ∩ {e, f, g, h, k}


(A U B′) ∩ B = {e, f}


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(g) (A U B) ∩ (A U B′)


hint: use parts a) and e)


(A U B) ∩ (A U B′) = {c, d, e, f, g, h, k} ∩ {a, b, c, d, e, f, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}



(A U B) ∩ (A U B′) = {c, d, e, f}