1.5 Set Operations

Chapter 1, section 5 Set Operations union intersection (relative) complement {difference}

Chapter 1, section 5 Set Operations Disjoint Sets For Example, A = {0,1} B = {2,3} A B = Ø –A and B are disjoint

Chapter 1, section 5 Set Operations Unions and Intersections Examples, given –A = {0,1,3} –B = {1,2,5} union (U) A U B = {0,1,2,3,5} intersection ( ): A B = {1}

Chapter 1, section 5 Set Operations DeMorgans Laws DeMorgans Laws: ~(A U B ) == ~A ~B ~(A B) == ~A U ~B

Chapter 1, section 5 Set Operations Distributive Properties A (B U C) == (A B) U (A C) A U (B C) == (A U B) (A U C)

Chapter 1, section 5 Set Operations Generalized Unions and Intersections Generalized unions and intersections A 1 U A 2 U … U A N = U A i *(similarly for intersections)

Chapter 1, section 5 Set Operations One final note on Sets Note: When N is infinity, then membership in the infinite union implies that there exists an N such that membership occurs in A N