Question

If X = {–5,1,3,4} and Y = {a,b,c}, then which of the following relations are functions from X to Y ?

• A. R${}_1$= {(–5,a), (1,a), (3,b)}
• B. R${}_2$= {(–5,b), (1,b), (3,a), (4,c)}
• C. R${}_3$ = {(–5,a), (1,a), (3,b), (4,c), (1,b)}
• D. R${}_4$ = {(-5,c), (-5,b), (1,a), (3,a), (4,b), (4,c)}

Answer 1

The correct option is B R${}_2$= {(–5,b), (1,b), (3,a), (4,c)}

Function is a special relationship where each input has a single output.
(i) R${}_1$ is not a function as '4' does not have an image in Y.

(ii) R${}_2$ is a function as each element of X has an unique image in Y.

(iii) R${}_3$ is not a function as '1' has two images in Y i.e 'a' and 'b'

(iv) R${}_4$ is not a function as '-5' and '4', has two images i.e 'b' and 'c'