Question

What are axioms?
A) Assumed universal truths in all branches of mathematics.
B) Assumed universal truths specific to geometry.
C) Assumed theorems.
D) Assumed definitions.

Answer 1

In this question, we have been asked what is an axiom? Find out what an axiom is and from which language this word has been derived from. Then choose the option which is closely related to the meaning of the axiom.

Complete step-by-step solution:
We have been asked the meaning of the axiom. Let us see what it means before moving towards the options to find the answer.
What are axioms?
‘Axioma’ is a Greek word which means “true without needing a proof”. The word axiom has been derived from this Greek word. Axioms are statements which are considered true without any mathematical proof. They are basically truths which help in other derivations. In addition to this, there is no evidence proving otherwise. All the mathematics depends on them.
For example: we know that. We know it is true and it does not need to be proven right. It is an axiom.
Now, we will move towards the question.
Option (B) says that axioms are assumed universal truths specific to geometry. However, axioms are not only limited to geometry. There are axioms based on all the branches of mathematics.

Therefore, our answer is option (A) Assumed universal truths in all branches of mathematics.

Note: Sometimes postulates are considered to be similar to axioms. However, axiom is a broader term and has statements for all branches in mathematics whereas postulates are for a particular branch, here, Geometry.
So the option (B) in this question means postulates.