**if a sequence is unbounded it will diverge**, this is **true**.

the contra positive of this statement is **if a sequence converges it is bounded,** is equivalent and thus also **true**

the inverse of this statement, that **if a sequence is bounded it will converge** is **false** (counterexample: 1,-1,1,-1,1,-1...)

and the converse of this statement that **if a sequence is diverges it is unbounded** is **false**

(counterexample 1,-1,1,-1,1,-1...)