Answer: So to find the set R in roster form, we need to identify the pairs (x, y) where x is an element of A y is an element of B, and x is relatively prime to y.
Given A = {2, 3, 4, 5} and B = {3, 6, 7, 10}, we need to determine which pairs satisfy the condition of being relatively prime.
Two numbers are relatively prime if their greatest common divisor (GCD) is 1. Let's check each pair (x, y) to see if x and y are relatively prime.
Pair (2, 3): GCD(2, 3) = 1 (relatively prime)
Pair (2, 6): GCD(2, 6) = 2 (not relatively prime)
Pair (2, 7): GCD(2, 7) = 1 (relatively prime)
Pair (2, 10): GCD(2, 10) = 2 (not relatively prime)
Pair (3, 3): GCD(3, 3) = 3 (not relatively prime)
Pair (3, 6): GCD(3, 6) = 3 (not relatively prime)
Pair (3, 7): GCD(3, 7) = 1 (relatively prime)
Pair (3, 10): GCD(3, 10) = 1 (relatively prime)
Pair (4, 3): GCD(4, 3) = 1 (relatively prime)
Pair (4, 6): GCD(4, 6) = 2 (not relatively prime)
Pair (4, 7): GCD(4, 7) = 1 (relatively prime)
Pair (4, 10): GCD(4, 10) = 2 (not relatively prime)
Pair (5, 3): GCD(5, 3) = 1 (relatively prime)
Pair (5, 6): GCD(5, 6) = 1 (relatively prime)
Pair (5, 7): GCD(5, 7) = 1 (relatively prime)
Pair (5, 10): GCD(5, 10) = 5 (not relatively prime)
Based on these calculations, we can see that the pairs (x, y) where x is relatively prime to y are:
(2, 3)
(2, 7)
(3, 7)
(3, 10)
(4, 3)
(4, 7)
(5, 3)
(5, 6)
(5, 7)
Therefore, the set R in roster form is:
R = {(2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6), (5, 7)}
(◕ᴥ◕) I hope this helps