Mathematics, 23.04.2021 16:30 sydneydavis57
Let the universal set be ℝ, the set of all real numbers, and let A = {x ℝ | −3 ≤ x ≤ 0}, B = {x ℝ −1 < x < 2}, and C = {x ℝ | 7 < x ≤ 9}. Find each of the following: (a) A ∪ B x ℝ −3 ≤ x < 2 x ℝ −3 < x ≤ 2 x ℝ x ≤ −3 or x > 2 x ℝ x < −3 or x ≥ 2 ∅ (b) A ∩ B x ℝ −1 ≤ x < 0 x ℝ −1 < x ≤ 0 x ℝ x < −1 or x ≥ 0 x ℝ x ≤ −1 or x > 0 ∅ (c) Ac x ℝ −3 < x < 0 x ℝ −3 ≤ x ≤ 0 x ℝ x ≤ −3 or x ≥ 0 x ℝ x < −3 or x > 0 ∅ (d) A ∪ C x ℝ −3 ≤ x ≤ 0 or 7 < x ≤ 9 x ℝ −3 < x < 0 or 7 < x ≤ 9 x ℝ −3 ≤ x ≤ 0 or 7 < x < 9 x ℝ −3 ≤ x ≤ 0 and 7 < x ≤ 9 ∅ (e) A ∩ C x ℝ −3 ≤ x ≤ 0 or 7 < x ≤ 9 x ℝ −3 < x < 0 or 7 < x ≤ 9 x ℝ −3 ≤ x ≤ 0 or 7 < x < 9 x ℝ −3 ≤ x ≤ 0 and 7 < x ≤ 9 ∅ (f) Bc x ℝ −1 ≤ x ≤ 2 x ℝ x ≤ −1 or x ≥ 2 x ℝ x ≤ −2 or x ≥ 1 x ℝ −1 < x < 2 x ℝ x < −1 or x > 2 (g) Ac ∩ Bc x ℝ x < −3 or x ≥ 2 x ℝ x ≤ −3 or x > 2 x ℝ −3 ≤ x ≤ 2 x ℝ x < −2 or x ≥ 3 x ℝ −3 < x < 2 (h) Ac ∪ Bc x ℝ x ≤ 0 or x > 1 x ℝ −1 < x < 0 x ℝ −1 ≤ x ≤ 0 x ℝ x < −1 or x ≥ 0 x ℝ x ≤ −1 or x > 0 (i) (A ∩ B)c x ℝ x < −1 or x ≥ 0 x ℝ −1 ≤ x ≤ 0 x ℝ −1 < x < 0 x ℝ x ≤ −1 or x > 0 x ℝ x ≤ 0 or x > 1 (j) (A ∪ B)c x ℝ −3 ≤ x ≤ 2 x ℝ x < −3 or x ≥ 2 x ℝ −3 < x < 2 x ℝ x < −2 or x ≥ 3 x ℝ x ≤ −3 or x > 2
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Let the universal set be ℝ, the set of all real numbers, and let A = {x ℝ | −3 ≤ x ≤ 0}, B = {x ℝ −1...
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