Which of the functions in exercise 2 of Section 51 are oneto

Which of the functions in exercise 2 of Section 5.1 are one-to-one? Which are onto?

Exercises

2. (a) Let f be the relation represented by the following graph. Is f a function
from A to B?
(b) Let W be the set of all words of English, and let A be the set of all
letters of the alphabet. Let f = {(w, a) ? W × A | the letter a occurs
in the word w}, and let g = {(w, a) ? W × A | the letter a is the first
letter of the word w}. Is f a function from W to A? How about g?
(c) John, Mary, Susan, and Fred go out to dinner and sit at a round
table. Let P = {John, Mary, Susan, Fred}, and let R = {(p, q) ?
P × P | the person p is sitting immediately to the right of the person
q}. Is R a function from P to P?

lcense plate number of the car c is s). Is L a function from C to S? 2 (a) Letf be the relation represented by the following graph. Is f a function from A to B? d. (b) Let W be the set of all words of English, and let A be the set of all letters of the alphabet. Let f = {(u, a) E W x A l the letter a occurs in the word w), and let g = {(u, a) e w x A l the letter a is the first letter of the word w. Is f a function from W to A? How about g? (c) John, Mary. Susan, and Fred go out to dinner and sit at a round table. Let P = {John, Mary, Susan, Fred), and let R= {(p.qe P x P I the person p is sitting immediately to the right of the person gl. Is R a function from P to P?

Solution

a)

No it is not as d has no image in B under f

b)

f is not a function because any words with 2 or more letters will map to more than one element in A

eg. on will map to o and n

g is a function as any words has only 1 first letter so any word maps to only one letter in A

c) Yes it is a function since it is a round table so every person has someone sitting to its immediate right. And there is only one person sitting to immediate right.