Direct Proof: If a|b and b|c, then a|c

This video provides an example of a direct proof.

[lifeproject]

Thanks for the solution and explanation, it helps me a lot.

[keldonchase]

Would this work?

Let {a, b, c, k, j, m} all be integers.

GIVENS: a|b ak = b a = b/k

GIVENS: b|c bj = c

PROVE: a|c am=c m = c/a

To prove that a|c, we would have to show that m is an integer.

We have to show that (c/a) simplifies to be an integer.

c/a

bj / (b/k)

Copy Dot Flip

bj * (k/b)

j*k

Integers Closed Under Multiplication

We find that m was an integer.

Thus, it is true that a|c.


I would really appreciate a response, thank you so much!!