Question 191247: Several of us in class are having problems with sets, subsets, etc. This question was placed on the board for us to solve. I so need help with this please.
Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}. List the elements of set
(a) A U B
(b) A ∩ B
(c) A′ ∩ B′
(d) A′ U B′
(e) A U B′
(f) (A U B′) ∩ B
(g) (A U B) ∩ (A U B′)
Answer by user_dude2008(1862)   (Show Source):
You can put this solution on YOUR website! 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}
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