Which of the following are binary operations? Tell me if my answers are correct

ID: 2900703 • Letter: W

Question

Which of the following are binary operations?

Tell me if my answers are correct and why if they are wrong please.

1) Addition on the set of all numbers that equal 0 modulo 10: Yes

2) Multiplication on the set of all numbers that equal 0 modulo 10: Yes

3) Addition on the set of all integers that are relatively prime to 5: No

4) Multiplication on the set of all integers that are relatively prime to 5: Yes

5) Addition on the set of prime numbers: No

6) Taking the GCD on the set of all negative integers:

7) Taking the GCD on the set of all integers bigger than 10:

8) Taking the LCM on the set of all positive integers less than 10:

9) Taking the LCM on the set of all even integers:

10) Taking the GCD on the set of all odd integers:

11) Taking the GCD on the set of all even integers:

For 6 to 11 I don't know how to start...

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