please answer these

. Using laws of set theory show that {AuB)nC = (Zumu). . Let A, B, and C he sets. Show that (AC)(CB)=. Draw Venn diagrams for the left hand side expression. . What can you say about the sets A and B if we know that A B = A? Prove your answer. . Show that for any sets A and B A A B = A A B. Draw Venn diagrams for both expressions. . Make a list of pairs, construct the matrix, and draw the graph of the relation R from the set A = {0,1,2,3,4} to the set B = {0,1,2,3} such that ((1,5) 6 R if and only if a + b = 5. . Prove that AxBx{AUC)=(AXBXA)U(AXBXC). . Let R be the relation on 2+ >