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Set builder form of the relation
R equals open curly brackets open parentheses negative 2 comma negative 7 close parentheses comma open parentheses negative 1 comma negative 4 close parentheses comma open parentheses 0 comma negative 1 close parentheses comma open parentheses 1 comma blank 2 close parentheses comma open parentheses 2 comma blank 5 close parentheses close curly brackets is

  1. left curly bracket open parentheses a comma b close parentheses colon b equals 2 a minus 3 semicolon a comma b comma element of Z right curly bracket  
  2. left parenthesis open parentheses x comma y close parentheses colon y equals 3 x minus 1 semicolon x comma y element of Z right curly bracket  
  3. left curly bracket open parentheses a comma b close parentheses colon b equals 3 a minus 1 semicolon a comma b element of N right curly bracket  
  4. left curly bracket open parentheses u comma upsilon close parentheses colon upsilon equals 3 u minus 1 semicolon minus 2 less or equal than u less than 3 blank a n d blank u element of Z right curly bracket  

The correct answer is: left curly bracket open parentheses u comma upsilon close parentheses colon upsilon equals 3 u minus 1 semicolon minus 2 less or equal than u less than 3 blank a n d blank u element of Z right curly bracket


    Let R equals open curly brackets open parentheses x comma y close parentheses colon y equals a x plus b close curly brackets. Then,
    open parentheses negative 2 comma negative 7 close parentheses comma left parenthesis negative 1 comma negative 4 right parenthesis element of R
    rightwards double arrow negative 7 equals negative 2 a plus b and negative 4 equals negative a plus b
    rightwards double arrow a equals 3 comma b equals negative 1
    therefore y equals 3 x minus 1
    Hence, R equals left curly bracket open parentheses x comma y close parentheses colon y equals 3 x minus 1 comma negative 2 less or equal than x less than 3 comma x element of Z right curly bracket

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