Problem 13.1
Which of the following sets are equal?
(a) {a, b, c, d}
(b) {d, e, a, c}
(c) {d, b, a, c}
(d) {a, a, d, e, c, e}
Problem 13.2
Let A = {c, d, f, g}, B = {f, j}, and C = {d, g}. Answer each of the following questions. Give reasons for your answers.
(a) Is B ⊆ A?
(b) Is C ⊆ A?
(c) Is C ⊆ C?
(d) Is C is a proper subset of A?
Problem 13.3
(a) Is 3 ∈ {1, 2, 3}?
(b) Is 1 ⊆ {1}?
(c) Is {2} ∈ {1, 2}?
(d) Is {3} ∈ {1, {2}, {3}}?
(e) Is 1 ∈ {1}?
(f) Is {2} ⊆ {1, {2}, {3}}?
(g) Is {1} ⊆ {1, 2}?
(h) Is 1 ∈ {{1}, 2}?
(i) Is {1} ⊆ {1, {2}}?
(j) Is {1} ⊆ {1}?
Problem 13.4
Let A = {b, c, d, f, g} and B = {a, b, c}. Find each of the following:
(a) A ∪ B.
(b) A ∩ B.
(c) A − B.
(d) B − A.