Easy
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.
$(i)$ 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.
(A) The given system of axioms is consistent.
$(i)$ This is Euclid's first axiom: 'Things which are equal to the same thing are equal to one another.'
$(ii)$ This is Euclid's second axiom: 'If equals are added to equals,the wholes are equal.'
$(iii)$ This is Euclid's third axiom: 'Things which are double of the same thing are equal to one another.'
Since all the given statements are standard axioms defined by Euclid,they do not contradict each other and are therefore consistent.
$(i)$ This is Euclid's first axiom: 'Things which are equal to the same thing are equal to one another.'
$(ii)$ This is Euclid's second axiom: 'If equals are added to equals,the wholes are equal.'
$(iii)$ This is Euclid's third axiom: 'Things which are double of the same thing are equal to one another.'
Since all the given statements are standard axioms defined by Euclid,they do not contradict each other and are therefore consistent.
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