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Question

Let $X equals left curly bracket 1 comma blank 2 comma blank 3 comma blank 4 comma blank 5 right curly bracket$ and $Y equals open curly brackets 1 comma blank 3 comma blank 5 comma blank 7 comma blank 9 close curly brackets.$ Which of the following is/are not relations from $X$ to $Y$ ?

(a) $R_{1} = {(x, y) | y = 2 + x, x \in X, y \in Y}$
$R_{2} = {(1,1), (2,1), (3,3), (4,3), (5,5)}$
$R_{3} = {(1,1), (1,3), (3,5), (3,7), (5,7)}$
$R_{4} = {(1,3), (2,5), (2,4), (7,9)}$

The correct answer is: $R subscript 4 end subscript equals left curly bracket open parentheses 13 close parentheses comma open parentheses 25 close parentheses comma open parentheses 24 close parentheses comma left parenthesis 79 right parenthesis right curly bracket$

$R subscript 4 end subscript$ is not a relation from $A$ to $B comma$ because $left parenthesis 79 right parenthesis element of R subscript 4 end subscript$ but $left parenthesis 79 right parenthesis not an element of A cross times B$

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