1. Express the following sets using the roster form:
(a) {x ∈ N | 25 ≤ x2 < 50}
(b) {x ∈ Z | 25 ≤ x2 < 50} Hint: This set is different than (a).
(c) {3n : n ∈ Z and − 1 ≤ n ≤ 2}
(d) {3n ∈ Z : −1 ≤ n ≤ 2} Hint: This set is different than (c).
2. Use set builder notation to give a description of the set {−10, −5, 0, 5, 10, 15}.
3. List the members, i.e. elements, of the following sets.
(a) {x, {y}, {x, y}}
(b) P({x, {y}, {x, y}})
4. Let A = {1, 2, 5, 6, 7} and B = {2, 3, 4, 7, 8}. Find the following sets.
(a) A ∩ B
(b) A ∪ B
(c) A − B
(d) B − A
(e) A under the assumption that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
5. Use Venn diagrams to verify the identity A ⊕ B = (A ∪ B) − (A ∩ B). Moreover, clearly
identify each region of the identity in your responses. That is, don’t just identify the final regions
of the left and right hand sides; show how the final region is formed.
6. Let A = {1, 2, 3, 4} × {1, 2, 3}.
(a) What is the cardinality of A?
(b) Define the subset B of A as B = {(s, t) ∈ A : s ≤ t}. List the elements of B.
