Need help!!

Question 1. Prove that for all sets A, B, and C, if A C B and B C C, then A C C. Question 2. Prove that for all sets A and B, if A - B = , then A C B. Question 3. Draw Venn diagrams for each of the sets below. (a) A - (B UC) (b) (B UC) O A Question 4. Prove or disprove: For all sets A and B, A - (A n B) = A - B. Make sure you justify each step. Question 5. Prove or disprove: For all sets A and B, if A S (B U C), then A C B or A C C. Question 6. Prove or disprove: For all sets A and B, if A S (B n C), then A C B and A C C. Question 7. Prove or disprove: For all sets A, B, and C, [(A U B) - C] U [C - (A U B)] = [(C - A) n (C - B)] U [(A - C) U (B - C)]. Question 8. Perform each calculation or explain why it is impossible. Show your work. I am unable to put the big brackets around the matrices, but hopefully it is clear. Given: A = 7 -2 9 -2 3 8 B = 590 4 2 -3C= 2 0 3 (a) 5A - B = (b) 2C + A = (c) AB = (d) AC = (e) CB =