Discrete math

Exercises to Sets Q1) Given the following: A UB= ( 7, 6, 5, 4, 3, 2, 1 } ANB= ( 7 ) BUC= { 8.7,5, 3, 2, 1) BNC = { 7,5,1} AUC= { 8, 7, 6, 5, 4, 2, 1 ) ANC-{7,2) 1) Find the sets A, B and C and 2) Draw the Venn Diagram 3) Find P(BU CI PA-BUC), P (A NB)- Q2) Simplify the following sets using Venn Diagram 1) AU (A-B) 5) BU (A-B) 2) A n(A-B) 6) A-(A-B) 3) A-(AUB) 4) A-(AUB) 7) (A UB) U(A-B) 8) (AUB) n(AB) 9) ( AB) U (A-B) 10) (A UB) - (B - A) 11)(A-B) n( AB) 12) ( AB)-(B-A) Q3) Draw Venn Diagram for the following sets 1) (A BUC 2) A (BUC) 3) AU BC 4) A U B 5) A B 6A NB 7)An (B-C) 8)(ANB) U (ANC) 9) (ANB) U (ANC) 10) A n Bnc Q4) Prove 1) if A B and C D then An CSBD 2) if An C SBC and ANC CBC then ACB Q5) Prove that (A-B) and (B-C) are disjoint Q6) Prove that (AUB) CUB = BC 1) using membership table 2) using set identities (laws) Q7) Prove AU (BNC) = (AUB) N (AUC) using 1) Venn Diagram 2) Membership table Q8) Show that if A, B and Care sets then | AUB UC = A +B+C - TAB-BOCANCI+ABC