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