laws and properties of sets
I B. COM UNIT 1 Laws and Properties of Sets: Sets have the following properties: 1. Commutative Laws: For any two sets A and B, A∪B=B∪A A∩B=B∩A. But A-B≄B-A 2. Associative Laws: For any three sets A, B, and C. A∪(B∪C)=(A∪B)∪C A∩(B∩C)=(A∩B)∩C 3. Distributive Laws: For any three sets A, B, and C. A∪(B∩C)=(A∪B)∩(A∪C) A∩(B∪C)=4. De Morgan’s Laws: For any two sets A and B, (A∪B) |=A|∩B| and (A∩B) |=A |∪B| For any three sets A, B, and C. A-(B∪C)=(A-B)∩(A-C) A-(B∩C)=(A-B)∪(A-C).A∩B)∪(A∩C) Example: 1 If A={1,2,3,4}, B={2,4,5,6} and C={1,3,5}, verify that A∩(B∪C)=(A∩B)∪(A∩C). Proof: Given that A={1,2,3,4}, B={2,4,5,6} and C={1,3,5} Consider, LHS A∩(B∪C) (B∪C)={2,4,5,6}∪{1,3,5} ={1,2,3,4,5,6} A∩(B∪C)={1,2,3,4}…………(1) (A∩B)= {1,2,3,4}∩{2,4,5,6}={2,4} (A∩C)= {1,3} (A∩B)∪(A∩C)= {1,2,3,4}………(2) A∩(B∪C)=(A∩B...