Discrete Mathematics Answers

Use set builder notation to give a description of each of these sets. a) {0, 3, 6, 9, 12} b) {−3,−2,−1, 0, 1, 2, 3} c) {m, n, o, p}

What is the cardinality of each of these sets? a) {a, 0, {a, 0}} b) {{a}} c) {∅, a, {a}} d) {0, 1, a, {a}, {a, {a}}}

Find the truth set of each of these predicates where the domain is the set of integers. a) P(x): 𝑥 3 ≥ 1 b) Q(x): 𝑥 3 = 8 c) R(x): x < 𝑥 2 d) F(x): |x +5| < 52

Let A, B, and C be sets. Show that a) (A ∪ B) ⊆ (A ∪ B ∪ C). b) (A ∩ B ∩ C) ⊆ (A ∩ B). c) (B − A) ∪ (C − A) = (B ∪ C) − A.

Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find a) A ∩ B ∩ C. b) A ∪ B ∪ C. c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.

What can you say about the sets A and B if we know that: a) A ∪ B = A? b) A ∩ B = A? c) A − B = A? d) A ∩ B = B ∩ A? e) A − B = B − A?

𝑈 = {𝑥|𝑥 ∈ 𝑅 ∧ 𝑥 > 14} 𝐴 = [−2, 25), 𝐵 = [15, 30]. Find: a) 𝐴̅̅̅∪̅̅̅𝐵̅ =?

Let R5 = {(1,2), (1,4), (1,6), (2,2), (2,4), (2, 6), (3,2), (3,4), (3,6), (4,2), (4,4), (4,6), (5,2), (5,4), (5,6)} and R6 = {(1,2), (1,4), (1,6), (2,4), (2,6), (3,6)} be relations. How many ordered pairs are there in R5 U R6?

Suppose a_n = 2ⁿ - 2*a_n-1 and a₀=0

What is a_2n?