A mathematical statement whose truth has been logically established is called a ____.

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Detailed Solution

A mathematical statement whose truth has been logically established is called a theorem.
We are given a mathematical statement; the truth has been logically established.
A mathematical statement can be either true or false, but can never be both.
Theorems are statements which are proved, using definitions, axioms, previously proved statements and deductive reasoning.
After Euclid stated his postulates and axioms, he used them to prove other results.
Then using these results, he proved some more results by applying deductive reasoning. The statements that were proved are called propositions or theorems.
Euclid deduced 465 propositions in a logical chain using his axioms, postulates, definitions and theorems proved earlier in the chain.
A mathematical statement which is proved using logic and other definitions is called a theorem. A theorem is always true.
Thus, a mathematical statement whose truth has been logically established is called a theorem.
Therefore, the correct answer is theorem.

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