Let A = {2, 3, 6, 7} and B = {4, 5, 6, 8}. Let R be a relation defined on A × B by (a1, b1) R (a2, b2)

Question

Let \(A=\{2,3,6,7\}\) and \(B=\{4,5,6,8\}\). Let R be a relation defined on \(A \times B\) by \(\left(a_{1},\ b_{1}\right) R\left(a_{2},\ b_{2}\right)\) is and only if \(a_{1}+a_{2}=b_{1}+b_{2}\). Then the number of elements in \( \mathrm{R}\) is _______.

Answer 1

Correct answer is : 25 

\(A=\{2,3,6,7\}\)

\(B=\{2,5,6,8\}\)

\(\left(a_{1}, b_{1}\right) R\left(a_{2}, b_{2}\right)\)

\(a_{1}+a_{2}=b_{1}+b_{2}\) 

\(\left.\begin{array}{l} 1.(2, 4)R(6,4)&2.(2, 4)R(7, 5)\\3.(2, 5)R(7,4)& 4.(3,4)R(6,5)\\5.(3,5)R(6, 4)&6. (3, 5) R (7, 5)\\7. (3,6) R (7, 4)&8. (3, 4) R (7, 6)\\9. (6, 5) R (7, 8)&10. (6, 8) R (7, 5)\\11. (7,8) R (7, 6) &12. (6, 8) R (6, 4)\end{array} \right]\times 2\\13. (6,6) R (6, 6)\)

Total \(24+1=25 \)