# 2. Prove that for all sets A and B, (A - B) N B = Ø. Proof (A Proof By Contradiction):

Let  Vi =    x  ℝ    −  1 i  ≤ x ≤  1 i    =    −  1 i ,  1 i    for each positive integer i. Find each of the following. (Enter your answers using interval notation.)   (a) ∪4i = 1Vi =    (b) ∩4i = 1Vi =     (c) Are V1, V2, V3, mutually disjoint? Explain. a.) Yes, because the intersection of the sets V1, V2, V3, ... is empty. b.) Yes, because no two of the sets V1, V2, V3, ... have any elements in common.     c.) Yes, because the union of the sets V1, V2, V3, ... is empty. d.) No, because no two of the sets V1, V2, V3, ... are disjoint. e.) No, because the sets V1, V2, V3, ... are disjoint.   (d) ∪ni = 1Vi =    (e) ∩ni = 1Vi =    (f) ∪∞i = 1Vi =    (g) ∩∞i = 1Vi =

For nonempty sets A, B, and C, let f: A-> B and g : B -> C. Prove: If gof is one-to-one, then f is one-to-one by each of the following methods: 1. 2. 3. a direct proof proof by contrapositive proof by contradiction

Answer these discrete math questions. Thank you :)