Theorem:

Theorem:

Let us learn about theorems and also about the procedure how a theorem is proved.A theorem is a generalised statement, which can be proved logically. A theorem has two parts, a hypothesis, which states the given facts and a conclusion which states the property to be proved. The two statements given above are examples of theorems.

Theorems are proved using undefined terms, definitions, postulates and occasionally some axioms from algebra.

In mathematics, a theorem is a statement which has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms. The derivation of a theorem is often interpreted as a proof of the truth of the resulting expression, but different deductive systems can yield other interpretations, depending on the meanings of the derivation rules. Theorems have two components, called the hypotheses and the conclusions.

A theorem is a generalised statement because it is always true. For example the statement or the proposition “If two straight lines intersect, then the vertically opposite angles are equal” is true for any two straight lines intersecting at a point. Such a statement is called the general enunciation.

In the theorem stated above, “two lines intersect” is the hypothesis and “vertically opposite angles are equal” is the conclusion. It is the conclusion part that is to be proved logically. To prove a theorem is to demonstrate that the statement follows logically from other accepted statements, undefined terms, definitions or previously proved theorems.

Hope you like the above example of Theorems.Please leave your comments, if you have any doubts.