For problems 2-4 use the following definitions. A = {0,1,8}, B = {0,2,4,6,8,10}, C ={{0},{1,8}},S={x|x∈Z∧3x≤4},and T={2x−1|x∈Z}. Remember that Z = {. . . − 2, −1, 0, 1, 2, . . .} and N = {0, 1, 2, 3, . . . }.

2. (7 points) Give examples of the following. If no example exists, explain why. (a) a subset of T

(b) an element of P(B)

(c) an element of A ∩ B
(d) an element of A × B
(e) ) a function from Z to N that is neither one-to-one nor onto (f) a function from A to B that is not one-to-one
(g) a function from B to A that is not onto

4.(8 points) Compute the following.

(a) A∩T
(b) Bc (For this part, assume that the universal set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.)

(c) (A∩B)-{−1,0,1} (d) A∩(B-A)
(e) g(4)
(f) |C|

(g) |P(B)|

(h) |B×B|