3.2. SUBSETS 3.2 Subsets Definition 3.2.1 A and B are sets and if A is a subset of B, denoted as ACB, if every element of A is also an element of B. (A is contained in B or B contains A.) Set A is a proper subset of set B, denoted as ACB, if set A is a subset of set B and sets A and B are not equal (A = B). A is not a subset of B, AB if and only if there is at least one element of A that is not an element of B. Note: Empty set is a subset of all sets) but not a proper subset of itself. 87 EXAMPLE 3.6 (The empty set as a subset) Given: A = { } and B = {1, 2, 3, 4, 5). Is ACB? Is A a proper subset of B? Yes EXAMPLE 3.7 Given: A = {0, 2, 4, 6, 8} and B = {8,0, 6, 2, 4}. Is A a subset of B? Is A a proper subset of B? Yes >1 INS EXAMPLE 3.8 Given: C = {1}, and D = {{1}, {4}} Is C a subset of D?

Fxample 3.7 Given- A{0,2,4,6,5) and B={5,0,6,2,4}. In A a nhare of B P Is A a proper aboct of d