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.

Answer 1

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)}