Which of the following are accepted without proof in a logical system? A.Axioms B.Theorems C.Postulates D.Common Notions
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In a logical system, axioms and postulates are the mathematical truths that are accepted without proof.
An axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful.
A postulate is an assumption, that is, a proposition or statement that is assumed to be true without any proof. Postulates are the basic structure from which lemmas and theorems are derived.
For the given situation,
Mathematicians assume that axioms are true without being able to prove them.
Postulates are the basic structure from which lemmas and theorems are derived.
From the definition, axioms and postulates are the mathematical truths that are accepted without proof.
Hence we can conclude that in a logical system, axioms and postulates are the mathematical truths that are accepted without proof.
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