The universal set in these problems is U = {−10, −9, −8, . . . 18, 19, 20}. Note that this set is not symmetric around 0. Define the following sets in universe: A = {−9, −7, −3, −2, 1, 7, 8, 16, 20} B = {x ∈ U : x ≤ 5} C = {x ∈ U : x is even} D = {x ∈ U : |x| ≥ 8} (a) List B, C and D in roster notation.

The universal set in these problems is U = {−10, −9, −8, . . . 18, 19, 20}. Note that this set is not symmetric around 0. Define the following sets in universe: A = {−9, −7, −3, −2, 1, 7, 8, 16, 20} B = {x ∈ U : x ≤ 5} C = {x ∈ U : x is even} D = {x ∈ U : |x| ≥ 8} (a) List B, C and D in roster notation.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Let A = {-30, -10, 10, 30, 50} and B = {-20, -10, 0, 10} be subsets of the universal set ε = {10x x € ZZ and -3≤ x <6}. (a) List the elements of An B and (AUB)'. (b) Evaluate: (i) │A\ B|; (ii) |A × B|; [1] (iii) |P(A)|; (iv) P(B) × P(A)|. [2] (c) Are the following statements are true or false? Explain your reasoning. (i) 0 СА; (ii) {0} = P(A); (iii) {10} E AUB; (iv) {10} is a proper subset of An B. (d) List the elements of P(A) P(B). [2] [2] (e) If the set C is also a subset of Ɛ, with |C| = 5, An C = {-10, 30} and BNC {-10, 20}, list the elements of C. = [2]