Question:
A = [1, 2, 3, 5] and B = [4, 6, 9]. Define a relation R from A to B by R = {(x, y) : the difference between x and y is odd, x ∈ A, y ∈ B}. Write R in Roster form.
Solution:
A = [1, 2, 3, 5] and B = [4, 6, 9]
R = {(x, y) : the difference between x and y is odd, x ∈ A, y ∈ B}
For x = 1,
$4-1=3$ and $6-1=5$
y = 4, 6
For x = 2,
$9-2=7$
y = 9
For x = 3,
$4-3=1$ and $6-3=3$
y = 4, 6
For x = 5,
$5-4=1$ and $6-5=1$
y = 4, 6
Thus, we have:
R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}