That is also known as "FOR EACH", though in some programming languages it is simply written as FOR. It means that a group of statements are to be executed once FOR EVERY item in a set. For example (depending on the programming language), that might be once for every array element.
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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".
To disprove this all you need to do if find one example of a prime that is not even. Such an example is called a counterexample. If a statement that all such and such or every such and such has a certain property, all you have to do to disprove it it to demonstrate the existence of on such and such that lacks the property .
True.
The statement "equals" means that they are equal. If the word "equals" and its symbol " = " are a true statement, then the two sides are truly equal in every way.
true