Read the following axioms
Question:

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 things are equal to one another.

Check whether the given system of axioms is consistent or inconsistent.

Thinking Process

To check the given system is consistent or inconsistent, we have to find that whether we can deduce a statement from these axioms which

contradicts any axiom or not.

Solution:

Some of Euclid’s axioms are

(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 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 contradicts any axiom. So,

given system of axioms is consistent.

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