1. Union and Intersection of Sets

2. Definition - intersection The intersection of two sets A and B is the set containing those elements which are and elements of A and elements of B. We write A  B

3. Set Operators: Intersection Definition: The intersection of two sets A and B is the set that contains all elements that are element of both A and B. We write: A  B = { x | (a  A)  (b  B) } U AB

4. Example - intersection If A = {3, 4, 6, 8} and B = { 1, 2, 3, 5, 6} then A  B = {3, 6}

5. Example - intersection If A = { , , , , , , , ,  } and B = { , , , @, ,  } then A ∩ B = { ,  } If A = { , , , , , , , , } and B = { , , ,  } then A ∩ B = { , , ,  } = B

6. Example - intersection If A is the set of prime numbers and B is the set of even numbers then A ∩ B = { 2 } If A = {x | x > 5 } and B = {x | x < 3 } then A ∩ B = 

7. Example - intersection If A = {x | x < 4 } and B = {x | x >1 } then A ∩ B = {x | 1 < x < 4 } If A = {x | x > 4 } and B = {x | x >7 } then A ∩ B = {x | x < 7 }

8. Venn Diagram - intersection A is represented by the red circle and B is represented by the blue circle. When B is moved to overlap a portion of A, the purple colored region illustrates the intersection A ∩ B of A and B Excellent online interactive Excellent online interactive demonstrationdemonstration

9. Definition - union The union of two sets A and B is the set containing those elements which are or elements of A or elements of B. We write A  B

10. Set Operators: Union Definition: The union of two sets A and B is the set that contains all elements in A, B, r both. We write: A  B = { x | (a  A)  (b  B) } U AB

11. Example - Union If A = {3, 4, 6} and B = { 1, 2, 3, 5, 6} then A  B = {1, 2, 3, 4, 5, 6}.

12. Example - Union If A = { , , , , ,  } and B = { , , , @, ,  } then A  B = { , , , ,, , , , @,  } If A = { , , , ,  } and B = { , ,  } then A  B = { , , , ,  } = A

13. Example - Union If A is the set of prime numbers and B is the set of even numbers then A  B = {x | x is even or x is prime }. If A = {x | x > 5 } and B = {x | x < 3 } then A  B = {x | x 5 }.

14. Venn Diagram - union A is represented by the red circle and B is represented by the blue circle. The purple colored region illustrates the intersection. The union consists of all points which are colored or or red or blue or purple. Excellent online interactive Excellent online interactive demonstration demonstration A  B A∩BA∩B

15. Disjoint Sets Definition: Two sets are said to be disjoint if their intersection is the empty set: A  B =  U AB

16. Complement of a Set The complement of set A is denoted by A ’ or by A C. A ’ = {x| x is not in set A}. Example Say U={1,2,3,4,5}, A={1,2}, then A ’ = {3,4,5}.

17. Definition of Union All the numbers in all the sets. Example {1, 2, 3, 4, 5, 7, 9} Definition of Intersection The numbers that the sets have in common. Example {1, 3, 5}

18. Find the Union of Sets U and B. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40}

19. Set A: {1, 2, 3, 4, 7} Set B: {2, 3, 5, 6, 8} Set C: {2, 4, 5, 6, 7, 9} Intersection of A, B, C {2}