Question1.a. Is 4 = {4}? b. How many elements are in the set {3, 4, 3, 5}? c. How many elements are in the set {1,{1},{1,{1}}}? Question

Question2. a. Is 3 {1, 2, 3}? b. Is 1 {1}? c. Is {2}{1,{2},{3}}? d. Is {1}{1,{2}}?

Question 3- Let A = {4, 5, 6} and B = {5, 6, 7} and define relations R, S, and T from A to B as follows: For all (x, y) A B, (x, y) R means that x y. (x, y) S means that is an integer. T = {(4, 7), (6, 5), (6, 7)}. a. Draw arrow diagrams for R, S, and T . b. Indicate whether any of the relations R, S, and T are functions.

Question 4- Let E = {1, 2, 3} and F = {2, 1, 0} and define a relation T from E to F as follows: For all (x, y) E F, (x, y) T means that is an integer. a. Is 3 T 0? Is 1T (1)? Is (2, 1) T ? Is (3, 2) T ? b. Write T as a set of ordered pairs. c. Write the domain and co-domain of T . d. Draw an arrow diagram for T .