Worksheet Chapter 11: Introduction to Set

1. Fill in the blank: A set that contains no elements is called an ________ set.

2. Given universal set ξ = {x : x is an integer, 1 ≤ x ≤ 12} and set B = {multiples of 3}. Write set B' using listing method.

3. List all elements of set A = {x : x is a prime number and 10 < x < 25} and state n(A).

4. True or False: The empty set ϕ is a subset of every set.

5. True or False: If set X = {a, b, c}, then the set {a, b, c} is NOT a subset of X.

6. State whether each of the following statements is TRUE or FALSE: (a) 7 ∈ {prime numbers} (b) 9 ∈ {multiples of 2} (c) {2, 4} ⊂ {1, 2, 3, 4, 5}

7. Given set M = {p, q}. List all possible subsets of set M.

8. Given set S = {x, y, z}. How many possible subsets can be formed from set S?

9. A group of 30 students were surveyed. All 30 belong to universal set ξ. Set S represents students who speak Spanish. If n(S) = 18: (a) Find n(S'). (b) Describe in words what set S' represents.

10. Given ξ = {x : x is a whole number, x ≤ 15}, P = {even numbers}, and Q = {multiples of 5}. (a) List the elements of set Q. (b) Find n(P'). (c) Is Q ⊂ P? Give a reason.