i did use my poof to prove. im not sure im doing right.

Question

here is exercises:
'Suppose a,b,c are integers if a|b and a|c, then a|(b+c).'

my answer:
Proof. Suppose a|b ans a|c.
By Definition of divisibility. we know a|b means there is an integer x with b= ax.
Likewise, a|c means there is an integer y for which c= ay
Thus b+c=(ax+ay)= a(x+y)
therefore a|(b+c).

Answer 1

Looks good to me.

Answer 2

thank you..