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Easy

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?

  1. (a) R subscript 1 end subscript equals left curly bracket left parenthesis x comma y right parenthesis vertical line y equals 2 plus x comma x element of X comma y element of Y right curly bracket  
  2. R subscript 2 end subscript equals left curly bracket open parentheses 11 close parentheses comma open parentheses 21 close parentheses comma open parentheses 33 close parentheses comma open parentheses 43 close parentheses comma left parenthesis 55 right parenthesis right curly bracket  
  3. R subscript 3 end subscript equals left curly bracket open parentheses 11 close parentheses comma open parentheses 13 close parentheses comma open parentheses 35 close parentheses comma open parentheses 37 close parentheses comma left parenthesis 57 right parenthesis right curly bracket  
  4. 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  

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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