Question

explain when a system of axioms is called consistent?

Answer 1

An axiomatic system is said to beconsistent if it lacks contradiction, i.e. the ability to derive both a statement and its denial from the system's axioms. In an axiomatic system, an axiom is called independent if it is not a theorem that can be derived from other axioms in the system.

Answer 2

an Eximoatic system is said to if it lacks contradiction i. e. the ability to derive both a statement and its denial from the system axioms