Question

Prove or disprove the following statements. If each statement is not true, salvage by making changes to the hypothesis:
1. If a∈ℤ, then a|a
2. If each of a,b and c is in ℤ, a|b and b|c, then a|c.
3. If each of a,b and c is in ℤ, a|b and a|c then a|(b+c)

Answer 1

What does | mean?

Answer 2

"The statement that a divides b means there is an integer c such that b=ac."
So for example:
4 | 12 ? , we would say yes, 3 because 12=4*3.

Answer 3

Is that the exact definition or does it rely on modulo? B/c then 0|0 is undef.

Answer 4

yeah thats the exact definition