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 which of the given system of axioms consistent?

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Only (i) and (ii)

Only (i)

All three

Only (ii) and (iii)

answer is C.

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Detailed Solution

Let's analyze the given axioms:

(i) Things which are equal to the same thing are equal to one another. Comment: This is known as the transitive property of equality. It essentially states that if A = B and B = C, then A = C. This axiom seems self-consistent.

(ii) If equals are added to equals, the wholes are equal. Comment: This axiom is a basic property of arithmetic. If A = B and C = D, then A + C = B + D. This axiom is also self-consistent.

(iii) Things which are double of the same thing are equal to one another. Comment: This means if you double the same value, you get the same result. For instance, if A = B, then 2A = 2B. This is another basic arithmetic principle.

All three are consistent.

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