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A relation R is defined from the set {2, 3, 4, 5} to the set {3, 6, 7, 10} by: x R y if and only if x and y are coprime (i.e., gcd(x, y) = 1). What is the domain of R?

1. {2, 3, 5}
2. {3, 5}
3. {2, 3, 4}
4. {2, 3, 4, 5}

Correct answer: {2, 3, 4, 5}

Solution

For x=2: gcd(2,3)=1 ✓; for x=3: gcd(3,7)=1 ✓; for x=4: gcd(4,3)=1 ✓; for x=5: gcd(5,3)=1 ✓. Every element in {2,3,4,5} is coprime with at least one element in {3,6,7,10}, so the domain is the entire set {2,3,4,5}.

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