Determine whether the statement is true or false. Show or explain why.

If n is a natural number and 4 | n, then 8 | n.

Ok, have seen this question several times.

Have been ignoring it since I don't know what 4│n is supposed to mean.

Does it mean "n is divisible by 4" ?

Perhaps another math expert can confirm.

If it means as I stated, then your question can be expressed to say,
"If n is a natural number and n is divisible by 4, then n is divisible by 8"

Of course that statement is false.
e.g. n = 20
(All I need is one exception to rule out a generality)

Yes, it meant divisible by, or I am assuming so. That is how it was asked on paper. So, the answer isn't true.

For future posts, n/8 = n divided by 8.

To determine whether the statement is true or false, we need to consider the divisibility rules for 4 and 8.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, in the number 148, the last two digits are 48, which is divisible by 4, so 148 is divisible by 4.

However, a number is divisible by 8 if the number formed by its last three digits is divisible by 8. For example, in the number 148, the last three digits are 148, which is not divisible by 8, so 148 is not divisible by 8.

Since being divisible by 4 does not imply being divisible by 8, the statement "if n is a natural number and 4 | n, then 8 | n" is false.

In other words, if a number n is divisible by 4, it does not necessarily mean that it is also divisible by 8.