Read the following axioms: (i) Things which are equal to the same thing are equal to one another. (ii) If equals are added to equals, the wholes are equal. (iii) Things which are double of the same thing are equal to one another. Check whether the given system of axioms is consistent or inconsistent.

Question

Philoid · Accepted Answer

Some of the Euclid’s axioms are:

i: Things which are equal to same thing are equal to one another.

ii: If equals are added to equals, the wholes are equal.

iii: Things which are double of the same things are equal to one another.

Thus, given three axioms are Euclid’s axioms. So, here we cannot deduce any statement from these axioms which contains any axiom. So, given system of axioms is inconsistent.

Read the following axioms:(i) Things which are equal to the same thing are equal to one another.(ii) If equals are added to equals, the wholes are equal.(iii) Things which are double of the same thing are equal to one another.Check whether the given system of axioms is consistent or inconsistent.