False
False. It is proven to be true IF some axioms are assumed to be true. A mathematical statement can be proven to be true only after some axioms have been assumed.
No
The Answer: NO
No. In fact, it cannot be true.
No
No, the converse of the statement "If I am hungry then I am not happy" is "If I am not happy then I am hungry." While the original statement is assumed to be true, its converse does not necessarily follow that truth. The truth of the original statement does not guarantee the truth of its converse; there could be other reasons for not being happy that do not involve hunger.
No, it is not.
It’s no
There are many kinds of statement that are not theorems: A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be. A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication. A statement can be false. A statement can be self-contradictory for example, "This statement is false".
"In mathematics, a proof is a demonstration that if some fundamental statements (axioms) are assumed to be true, then some mathematical statement is necessarily true." (from Wikipedia)
No
No, it is not necessarily true