Q. 35.0( 3 Votes )
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A system of axiom is called consistent, if there is no statement which can be deduced from these axioms such that it contradicts any axioms.
We know that, if a transversal intersects two parallel line, then each pair of corresponding angles are equal, which is a theorem. So, statement (i) is false and not an axiom.
Also, we know that, if a transversal intersects two parallel line, then each pair of alternate interior angles are equal. It is also a theorem. So, statement(ii) is true and an axiom.
Thus, in given statements, first is false and second is an axiom.
Hence, given of axioms is not consistent.
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