Set Notation Practice

1 Secondary 4 Mathematics: Sets 1. Definition of a Set • A set is a collection of distinct objects such as numbers, letters, symbols, etc. • The objects in a set are called the members or elements of the set. • Common examples of sets (a) Set of whole numbers, W = {0, 1, 2, 3, …) (b) Set of integers, Z = {…, –2, –1, 0, 1, 2, …} (c) Set of prime numbers, P = {2, 3, 5, 7, 11, …} 2. Ways of Defining a Set (a) A = {a, b, c} à A is the set containing elements a, b and c. (b) B = {x : x is a prime number} à B is the set containing set of prime numbers - B can also be expressed as B = {2, 3, 5, 7, 11, …} (c) C = {x : x is a integer number such that 5 ≤ x <9} - C can also be expressed as C = {5, 6, 7, 8} 3. Null or Empty Sets • A null or empty set, denoted by { } or ∅, is a set which contains no elements. 4. Equal Sets • Two sets are equal if they have the same elements. Example: Set A = {1, 2, 3} and set B = {3, 1, 2} Then A = B (Note that the order in which the elements appear in the set is not important).

2 5. Subset and Subset Symbols Symbol Meaning Example A ⊂ B Set A is a proper subset of set B. i.e., every element of A is also an element of B, and A ≠ B. Set A = {1, 2, 3} and set B = {3, 1, 2, 4, 5}, then A ⊂ B 𝐴 ⊆ 𝐵 A is subset of B i.e., every element of A is also an element of B, and set A can be equal set B. If A ⊆ B and Set B = {3,1, 2, 4, 5}, then Set A can be = {1, 2, 3} or Set A can be = {1, 2, 3, 4, 5} 𝐴 ⊄ 𝐵 A is not subset of B. If Set A = {1, 2, 5} and Set B = {1, 3, 6, 8}, then 𝐴 ⊄𝐵 𝐴 ∩ 𝐵 The intersection of sets A and B. It refers to the common elements found in both sets. If Set A = {1, 2, 3} and Set B = {1, 3, 6, 8}, then 𝐴 ∩ 𝐵 = {1, 3} 𝐴 ∪ 𝐵 The union of sets A and B. This refers to the set of elements which belongs to either set A or set B or both/ If Set A = {1, 2, 3} and Set B = {1, 3, 6, 8}, then 𝐴 ∪ 𝐵 = {1, 2, 3, 6, 8} n(A) Represents the number of elements in set A. If Set A = {1, 2, 3}, then n(A) = 3 6. Element of a Set • If a is an element of set A, we write a ∈ 𝐴. • If b is not an element of set A, we write b ∉ A. 7. Universal Set • A universal set is a set which contains all the available elements in a particular discussion. • It is the largest set in the discussion and is denoted by ξ.

3 8. Complement of Set • The complement of a set A, denoted by 𝐴′, relative to the universal set ξ contains elements that are not elements of A but are elements of ξ. i.e. it is the set that contains all elements in 𝛏 except those in A. Example: If ξ = {1, 2, 3, 4, 5}, 𝐴 = {1, 2}, then 𝐴′ = {3, 4, 5} 9. Disjoint Sets • Two sets are said to be disjoint if they do not have any common element. Example: If A = {1, 2, 3, 4, 5}, 𝐵 = {6, 7}, then 𝐴 and 𝐵 are disjoint. 10. Venn Diagram • A Venn diagram is pictorial representation of relationships involving sets. Example: If ξ = {1, 2, 3, 4, 5, 6, 7, 8}, 𝐴 = {1, 2, 3, 4}, 𝐵 = {2, 3, 6, 7}. Venn diagram of example: Venn diagram of (1) proper subset, (2) disj