Source: Extra Practice
A relation R is defined from A = {2, 3, 4, 5} to B = {3, 6, 7, 10} by xRy if and only if 'x divides y'. The relation R in roster form is:
Options
Option A is correct
{(2, 6), (2, 10), (3, 3), (3, 6), (5, 10)}
Option B
{(2, 6), (2, 10), (3, 6), (5, 10)}
Option C
{(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}
Option D
{(2, 3), (3, 7), (4, 6), (5, 10)}
Explanation
We check each x ∈ A against y ∈ B: 2 divides 6 and 10; 3 divides 3 and 6; 4 divides nothing in B; 5 divides 10. Combining these, R = {(2, 6), (2, 10), (3, 3), (3, 6), (5, 10)}. Option B misses (3, 3). Option C is the inverse relation (yRx). Option D contains pairs where x does not divide y.