Mathematics

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 $$180^0$$.
Is this system of axioms consistent? Justify your answer.


SOLUTION
The given system of axioms is not consistent because if a ray stands on a line and the sum of two adjacent angles so formed is equal to $$180^0$$. then for two lines which intersect each other, the vertically opposite angles becomes equal. 
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Subjective Medium Published on 09th 09, 2020
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