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Theory:- A statement or principle devised to explain a group of facts especially one that has been repeatedly tested.
Law:- A statement describing a relationship observed to be invariable between or among phenomena for all cases in which the specified conditions are met: eg- the law of gravity.
Theorem:- (In this sense) A mathematical proposition that has been or is to be proved on the basis of explicit assumptions.
To know how they differ, first know how they are similar: They are all "Explanations".
Now, the difference:
Hypothesis - Tentative Explanation.
Theory - Verifiable Explanation.
Theorem - Demonstrable Explanation.
Law - Definite Explanation.
That, in a nutshell, is that. Now, don't ask me what's the difference between Verifiable and Demonstrable
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