ANTIGUA STATE COLLEGE FOUNDATION MATHEMATICS UNIT 1 – SET THEORY 2020 -2021 TUTORIAL SHEET 1 1. Write down five elements of each of the following sets. a. Rational Numbers b. Irrational Numbers c. Integers d. Whole Numbers. 2. Which of the following are integers 3 3, 4 , , 20 , , e, 23, 9 5 3. Consider these sets: A={x:x–4=3} B={x:x+7=5} C = { x : 5x = 8 } D = { x : 3x = 28 } E = { y : 4y = -12 } Which of the sets is a subset of the set of: a. Rational Numbers b. Integers c. Natural Numbers. 4. Write down three elements of each of the following sets, where x and y are whole numbers: 𝑥 2 a. H = {y : y = 5x } b. K = { y : y = 2x – 1} c. I = {𝑦: 𝑦 = 3 + 3} 5. Express the following intervals in set builder notation. a. (−∞, −5] b. (−3, ∞, ) c. (−10,50] d. [25, 180] 6. Let the universal set be the set of real numbers, ℝ. Let A and B be intervals defined by 𝐴 = (−7, 12] and 𝐵 = (−1, ∞). Using the number line find: a. 𝐴 ∩ 𝐵, state your answer in set builder notation b. (𝐴 ∩ 𝐵)′ , state your answer in interval notation 7. Let the universal set be the set of real numbers. If A and B are (−2, 5] and (−5, 7] respectively, then use interval notation to represent the following: a. 𝐴 ∪ 𝐵 d. 𝐴′ ∩ 𝐵 b. 𝐴 ∩ 𝐵 e. 𝐴 − 𝐵 c. 𝐴′ f. 𝐵 − 𝐴 8. Let the universal set be the set of real numbers ℝ. Represent the following sets on the real number line: 𝐴 = (−3, 4] and 𝐵 = (0, 12) . Express a. 𝐴 ∩ 𝐵 in set builder notation b. 𝐵 − 𝐴 in interval notation c. 𝐴 − 𝐵 in interval notation d. (𝐴 − 𝐵)′, in interval notation 9. Let the universal set be the set of real numbers ℝ . Given the intervals 𝑀 = (−∞, 120) and 𝑁 = (80, 200], express the following in both set builder and interval notation: a. 𝑀 ∪ 𝑁 b. 𝑀 ∪ 𝑁′ c. 𝑀 ∩ 𝑁′ d. M – N 10. Let the intervals A and B be defined as are (0, 18) and (7, ∞] respectively. Given that the universal set is ℝ, represent the following intervals in the specified notation: a. 𝐴 ∩ 𝐵 set-builder notation b. 𝐵′ set builder notation c. 𝐴 ∩ 𝐵′ interval notation d. (𝐴 ∩ 𝐵′)′ interval notation