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Question

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

${(a, b) : b = 2 a - 3; a, b, \in Z}$
$((x, y) : y = 3 x - 1; x, y \in Z}$
${(a, b) : b = 3 a - 1; a, b \in N}$
${(u, υ) : υ = 3 u - 1; - 2 \leq u < 3 a n d u \in Z}$

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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