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  • Read the following two statements which are taken as axioms: (i) If two lines intersect each other, then the vertically opposite angles are not equal. (ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°. Is th

Read the following two statements which are taken as axioms:

(i) If two lines intersect each other, then the vertically opposite angles are not equal.

(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.

Is this system of axioms consistent? Justify your answer.

Answers (1)

Given system of axioms is not consistent.

Solution:

Axiom: A statement or proposition which is regarded as being self-obviously evident, established or accepted. Hence, it is accepted without controversy or question.

Statement (i) is False

We know that if two lines intersect each other, then the vertically opposite angles are equal. This is a theorem.

Theorem: A statement or proposition not plainly obvious but rather demonstrated by a chain of reasons; a fact set up by methods for acknowledged certainties

Statement (ii) is true

We know that, if a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°. It is an axiom.

Thus (i) statement is not an axiom and (ii) statement is an axiom.

Hence given system of axioms is not consistent.

 

 

 

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