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Math 2305 / Summer II 2023 / Student's Name: Week 2 Practice (1) / July 17 / Instructor: Youn-Sha Chan Problem(1) (6 points) The symmetric difference of A and B, denoted by A DB, is the set containing those elements in either A or B, but not in both A and B. (a) Find the symmetric difference of A = {3, 5, 7} and B = {1, 2, 3, 4, 5}. (b) Draw a Venn diagram for the symmetric difference of the sets A and B. (c) List all subsets of set A. Problem(2) (8 points) Give an example of a function from N to N that is a) one-to-one but not onto. b) onto but not one-to-one. c) both onto and one-to-one (but different from the identity function). d) neither one-to-one nor onto. Problem (3) (5 points) Find the inverse function of y = f(x) = 3x - 7. Problem(4) (6 points) Use mathematical induction to show that [k2 _ n(n + 1) (2n+ 1 ) VnEN. 6 Problem(5) (12 points) Find the following sums: (a) Ek-1 (3k - 2) ( b) [k= 1 (c) 20 (d) ER=1 (3 ) k Problem(6) (20 points) Given A - -3 3 , B-| 3 4]. 0- [8 -8 -3], and -5 D = u = [_ ]]. v= [ 31, and w-? (a) Find A + B. (b) Find AB. (c) Find A-1. (d) Find ABC. (e) Find D (utv). (f) Find C w. (g) Find CD. (h) Find SVT. (i) Find SAT. (j) Find SOT. (k) Find (SOT) (2) and (SOT) 13]