Question

Let the relation R is defined in N by \(a \mathbb{R} b\), if \(3a+2b = 27\) , then R is

• A. {(1,12), (3,9), (5,6), (7,3)}
• B. {(1,12), (3,9), (5,6), (7,3), (9,0)}
• C. \(\{(0, \frac{27}{2}), (1,12), (3,9), (5,6), (7,3)\}\)
• D. {(2,1), (9,3), (6,5), (3,7)}

Answer 1

The Correct Option is A

To determine the relation R defined in N by a \(R_ b\), if \(3a + 2b = 27\), we need to find the pairs (a, b) that satisfy this equation.
Let's check each option to see which one represents the relation R.
Option (A): {(1, 12), (3, 9), (5, 6), (7, 3)}
Let's substitute the values from each pair into the equation:
\(3(1) + 2(12) = 3 + 24 = 27\) (satisfied)
\(3(3) + 2(9) = 9 + 18 = 27\) (satisfied)
\(3(5) + 2(6) = 15 + 12 = 27\) (satisfied)
\(3(7) + 2(3) = 21 + 6 = 27\) (satisfied)
So, option (A) represents the relation R.
Therefore, the relation R defined in N by a\( R_ b\), if 3a + 2b = 27, is {(1, 12), (3, 9), (5, 6), (7, 3)} (option A).