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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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Is every statement a theorem why?
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".
Prove and disprove the statement that every prime number is an even number?
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 .
Is this statement true or falseA lattice polygon is a figure on a grid with every vertex at a grid point?
True.
Are both sides of an equation equal in numeric value or units or dimentions?
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.
In a two column proof every new statement in the first column must be justified by a reason in the second column?
true
