Discrete Mathematical Structures by Pearson

1-4 Discrete Mathematical Structures

1.2.2 Subset

Let A and B be any two non-empty sets. The set A is called a subset of B if every element of A is

an element of B and we write A ⊆ B. Mathematically A ⊆ B if x ∈ A ⇒ x ∈ B.

1.2.3 Proper Subset

The set A is called a proper subset of B and is denoted by A ⊂ B if every element of A is an

element of B and there is at least one element in B that is not in A. For example

1. If A = {1, 2, 3} and B = {1, 2, 3, 4, 5}, then A ⊂ B.

2. If A = {2, 4, 6} and B = {6, 2, 4}, then each element of A is also an element of B and

there is no element of B that is not in A and so A is a subset of B. The sets A and ...