Discrete Mathematics Please show all work. 1. Let A (a, r, s, t) and B 17, 18, 1

Question

Discrete Mathematics Please show all work. 1. Let A (a, r, s, t) and B 17, 18, 19, 20). Determine which of the following are functions. Explain why or why not. a. f g: A × B, where f = {(q, 17), (r, 18), (s, 19), (t, 20)) b. g Ax B, where g-{(q, 17), (q, 20), (s. 19), (t, 20),(r, 20)) c. A × B, where h = {(q, 17), (r, 20), (s. 19), (t, 20)) d. k SBXB, where k={(17,17), (18,17), (19,17), (20,18)) IgA×A, where l-{(q, r), (q, s), (s, r), (t, t) e. 3. State whether each of these functions, where sets A and B are as stated in #1, are one-to-one, onto, both, or neither, and give a brief explanation for each answer: a. f A×B, where f={(q, 17), (r, 18), (s,19), (t, 20)} b. g A × B, where g (q, 17), (s. 19), (t, 20), (r, 20)) h A × B, where h = {(9, 17), (r, 20), (s, 17), (t, 20)) c. d. kgBxB, where k={(17,17), (18,17), (19,17), (20,17)) e. ISAx A, where l - [(q,r). (r,s), (s,q). (t, t))

Explanation / Answer

1.
a) it is a function. Function is a special kind of relation which gives exactly      one output for each input from domain.
b) Not a function

c) it is a function

d) it is a funation

e) Not a function

3.
a ) both (one to one and onto) (one to one - every element of codomain mapped to at most one in domain)
                                 (onto - every element of codomain mapped to at least one in domain)
                                 (onto - every element of codomain mapped to exactly one in domain)

b) one to one

c)neither

d)neither

e) both

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