Are the following operations defined on the sets given? Explain why!

Question

1. Multiplication on ℕ+

2. Multiplication on ℤ

3. LEN on ℕ

4. LEN on C

5. LEN on S

6. JOIN on S

Answer 1

ℕ+={1,2,3,4,5,6,7,...}

Is multiplication defined on this set?

The answer really depends on what you mean by defined on means. I suspect that you mean closed.

That is if you multiply any two of the numbers listed in the set above do you get a number in that set.

Think about when you were in elementary school. You only knew about 0 and 1 and 2 and 3 and 4 and... Well we just removed 0. If you multiply any number in the set above do you get another number in the set?

ℤ ={....-2,-1, 0, 1, 2. 3,...} Same question for these numbers.

I have no idea what LEN on ℕ, LEN on C, LEN on S and JOIN on S means.