2.2 Set Operations L Al-zaid Math1101.

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Presentation transcript:

2.2 Set Operations L Al-zaid Math1101

The Union DEFINITION 1 Let A and B be sets. The union of the sets A and B , denoted by AUB , is the set that contains those elements that are either in A or in B , or in both. This tells us that A U B = {x | x ϵ A V x ϵ B } . L Al-zaid Math1101

EXAMPLE 1 Find The union of the sets {1,3,5} and {1,2,3}. L Al-zaid Math1101

The Intersection DEFINITION 2 Let A and B be sets. The intersection of the sets A and B , denoted by A ∩ B , is the set containing those elements in both A and B . This tells us that A ∩ B = {x | x ϵ A Λ x ϵ B } . L Al-zaid Math1101

EXAMPLE 3 Find The intersection of the sets {1,3,5} and {1,2,3}. L Al-zaid Math1101

Disjoint Sets DEFINITION 3 Two sets are called disjoint if their intersection is the empty set. EXAMPLE 5 Let A = {1,3,5,7,9} and B = {2, 4, 6, 8 , 10} is disjoint or not. L Al-zaid Math1101

The Difference Of Two Sets DEFINITION 4 Let A and B be sets. The difference of A and B , denoted by A - B , is the set containing those elements that are in A but not in B . An element x belongs to the difference of A and B if and only if x ϵ A and x ɇ B . This tells us that A - B = {x | x ϵ A Λ x ɇ B } . L Al-zaid Math1101

EXAMPLE 6 Find The difference of {1,3,5} and {1,2,3} L Al-zaid Math1101

The Complement Of a Set DEFINITION 5 Let U be the universal set. The complement of the set A , denoted by Ā , is the complement of A. In other words Ā=U-A. An element belongs to Ā if and only i f x ɇ A . This tells u s that Ā = {x | x ɇ A } . L Al-zaid Math1101

Homeworks Page 130 3 (a,b,c,d) 14 19 25 (a,c) 59 L Al-zaid Math1101