Worksheet for Sets (Discrete Math) Answers
1. Let A = {a, b, c, d, e, f} B = {a, c, f}, and C = {b, c, d, g}. Find each of the following:
(a) A∪B = {a, b, c, d, e, f}
(b) A∩B = {a, c, f}
(c) A∪C = {a, b, c, d, e, f, g}
(d) A∩C = {b, c, d}
(e) A−B = {b, d, e}
(f) B−A = ∅
(g) B∪C = {a, b, c, d, f, g }
(h) B∩C = {c}
2. Let the universal set be the set R of all real numbers and let A = {x ∈ R | -1 < x < 3}, B =
{x ∈ R | 0 ≤ x ≤ 5}, and C = {x ∈ R | 1≤ x < 7}. Find each of the following:
(a) A∪B = { x ∈ R | -1 < x ≤ 5}
(b) A∩C = { x ∈ R | 1 ≤ x < 3}
(c) C−A = { x ∈ R | 3 ≤ x < 7}
(d) Ac = { x ∈ R | x ≤ -1 or x ≥ 3}
(e) Bc = { x ∈ R | x < 0 or x > 5}
(f) Ac ∪Bc = { x ∈ R | x < 0 or x ≥ 3}
(g) (A∪B)c = { x ∈ R | x ≤ -1 or x > 5}
3. True or False?
(a) Z+ ⊆ Q True
(b) Z− ∪ Z+ = Z False since zero is an integers but is not an element of (Z− ∪ Z+)
(c) Q ∩ R = Q True
(d) ∅∈{∅} True
(e) 0∈∅ False since an empty set, ∅, means that there is no element in it.
4. Let set A = {x, y, z}.
(a) List all the elements in the power set of (A).
(A) = {∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}
(b) How many elements in the power set of (A). 8
(c) Let a set X has n elements. How many proper subsets the set X has? 2n-1
