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Question

If X = {–5,1,3,4} and Y = {a,b,c}, then which of the following relations are functions from X to Y ?
  1. R1= {(–5,a), (1,a), (3,b)}
  2. R2= {(–5,b), (1,b), (3,a), (4,c)}
  3. R3 = {(–5,a), (1,a), (3,b), (4,c), (1,b)}
  4. R4 = {(-5,c), (-5,b), (1,a), (3,a), (4,b), (4,c)}


Solution

The correct option is B R2= {(–5,b), (1,b), (3,a), (4,c)}
Function is a special relationship where each input has a single output.
(i) R1 is not a function as '4' does not have an image in Y.

(ii) R2 is a function as each element of X has an unique image in Y.

(iii)  R3 is not a function as '1' has two images in Y i.e 'a' and 'b'

(iv) R4 is not a function as '-5' and '4', has two images i.e 'b' and 'c'

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