Problem pts$.)$

Expected Time: $30$ minutes.

Objectives: Practice with the Converse and Disproofs by Counter$-$example.

Claim. For every integer $n,$ if $3|n|$ then $3n+1.$

Note: As with problem $1,3|n|$ means $"3$ divides n$"$ and $3n$ means $"3$ does not divide $n".$

$($a$)(1$ pt$.)$ On brightspace, determine the converse of the claim.

$($b$)(1$ pt$.)$ On brightspace, determine whether the converse of the claim is true.

$($c$)(5$ pts$.)$ On brightspace, determine which of the given examples are counter$-$examples to the converse you stated in part $($a$).$

$($d$)(1$ pt$.)$ On brightspace, determine whether the following claim is true or false. No justification is necessary.

Claim. For every integer $n,$ if $2n+1$ then $2|n|.$