1. (5) Let A-lg,r,s,t and B- 17, 18, 19,20. Determine which of the following are
ID: 3910221 • Letter: 1
Question
1. (5) Let A-lg,r,s,t and B- 17, 18, 19,20. Determine which of the following are functions. Explain why or why not. a. f Ax B, wheref= {(9,17), (r, 18). (s,19),(s.20)) b. gSAx B,where g [(q, 17), (s, 19), (t, 18), (r,20)) c. hSA × , where h={(q, 17), (r, 20), (s. 19),(t,20)) d. ksBxB,where k={(17, 17), (18,17), (19,20), (20,18)) e. ISAx A,where-(r). r.s), (s,r).(t,t) 2. (5) Give the ranges of each of these functions where sets A and B are as stated in fçAx B. wheref={(q, 17),(r, 18), (t, 19),(s,20)) gSA × B,where g={(r, 17), (s. 19), (t,20), (q, 20)) hSAx B,where h ((q,17), (r, 17), (s, 17), (t, 20)) a. b. c. d. kçBX B. where k=((17,18), (18,18), (19,18), (20,18): e. ISAx A, where l(q.r).(r,s), (s, t).(t,q))Explanation / Answer
1)
Relation A-->B is a function only when every element in A map to unique element in B.
that means, needed mapping for every element in A with any unique element in B. and one or more elements in A can map to same element in B. but a element in A can't map to more than one element in B.
Relation AXB = {(q,17),(q,18),(q,19),(q,20),(r,17),(r,18),(r,19),(r,20),(s,17),(s,18),(s,19),(s,20),(t,17),(t,18),(t,19),(t,20)}
a) every element in f have image in AXB. So its a function.
b) every element in g have image in AXB. so its a function.
c) every element in h have image in AXB. so its a function.
d) every element in k have image in AXA. so its a function.
f) every element in l have image in BXB. so its a function.
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