Question

Question about implications

Answer 1

The first one: An integer n is divisible by 6 whenever 4n is divisible by 6.

Answer 2

I said, it was false.
The converse is: If an integer n is divisible by 6 then 4n is divisible by 6. Which I said was true.

Answer 3

The contrapositive (which must be false if the original is false) is:
If an integer n is not divisible by 6 then 4n is not divisible by 6.

Answer 4

Then I have to explain. This is where I am somewhat confused I guess?

Answer 5

I was going to say: since the original is false, the converse must be true. But in the next example, the original is false and so is the converse. So that isn't a good enough reason I don't think.

Answer 6

The contrapositive is "if an integer 4n is not divisible by 6, then n is not divisible by 6." Which is easier to explain, because it's correct. :-)