Prove forall a, b, c elementof z^+, if a|(b + c) and a|c then a|b.

Answer with explanation:

If A is a positive Integer , then if A divides B , then in terms of equation it can be written as

→B=A m ,where m is any integer.

⇒Now, it is given that , three elements , a , b and c belong to set of Integers.

a divides b+c,and  a divides c

then we have to prove that , a divides b.

Proof

→b+c= k a,where k is an integer , as b+c is divisible by a.

→Also, c= m a, where m is an integer.Because c is divisible by a.

→b+ m a= k a

→b=k a - ma

→b=a (k -m)

Since, k and m are both integers.So , k-m will be also an integer.

Let, k-m =p

→b=a p

which shows that , b is divisible by a.

Hence proved.

the answer is a

step-by-step explanation: