(a) Let f be the relation represented by the following graph. Is f a function fr

Question

(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?

Explanation / Answer

A function is a special relationship where each input has a single output

a> yes F is a function .Since the values in set A {a , b , c} have unique image that is elemetns of set B {x,y} , the relation f is a function.

b> there wll be a lot of words in the set W which start with the letter a . So the element of set A will mave multiple images in the set W . so f is not a function .

Like wise there will be multiple words n the set W whose first letter is a , so there are multiple outputs for a single inout . Hence g is not a function.

c > yes R is a function from P to P

this is because at a round table a person q will have just 1 person sitting to his/her immediate right .

In fact the fuction is both one wto one and onto .

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