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1313_section6o1

# 1313_section6o1 - Section 6.1 Sets and Set Operations A set...

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Section 6.1 – Sets and Set Operations 1 Section 6.1 Sets and Set Operations A set is a collection of objects. An element is an object of a set. Notation: = “element of” = “not an element of” Example: Let A be the set of all prime numbers. 2 is an element of A and 3 is an element of A ; but, 4 is not an element of A . A 2 , A 3 , A 4 The set C = { x | 4 2 = x } is in set builder notation . The set C can also be written as follows: C = {-2, 2}. Let A and B be two sets. If every element of A is also in B , A is said to be a subset of B . Notation: = “subset of” / = “not a subset of” Example: Let A be the set of all prime numbers and B be the set of all integers. Then, A is a subset of B . B A Example 1: Let C = {1,2,3,4,5,6}, D = {2,4,6}, E = {2,1,6,4,3,5}, and G = {1, 4, 6}. Which of the following is/are true? I. D C II. E / C III. D G The set A is a proper subset of a set B (Notation: B A ) if the following two conditions hold. 1. B A 2. There exists at least one element in B that is not in A .

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