Question

prove that ( A U C) * ( BU D ) =( A*B)U( C*D )​

Answer 1

Answer:

Question 1. Show that (A x B)U(C x D) C (AUC) (BUD). Question 2. Prove that for all sets A, B, if AUB=A B9 A = B. Question 3. Prove or disprove the following: For any sets A, B, and C we have (a) (AUB) - C = (AUC)-(BUC) (b) (A x B = AXBO Problem 4. Let A be a set of integers, and let y be the relation on AX A defined by (a,b) (c,d) if a +d=b+c. (a) Prove that is an equivalence relation. Problem 5. Solve each of the following inequalities and mark the solution set on the real line as well as express the solution set as an interval or as the union of intervals: (1) -2 +3 +2 > 3,(2) (3x +1)< (x + 1) (3) x2(- 1)(x + 4) <0