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Q.

Which of the following is not an axiom of Euclid?

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a

Things which are equal to the same thing are equal to one another.

b

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

c

If equals are subtracted from equals, the remainders are equal.

d

If equals are added to equals, the wholes are unequal.

answer is D.

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Detailed Solution

   The axioms of Euclid are as follows:

  • Things that are equal to the same thing should be equal to each other.
  • When equals are added to equals then, the whole’s are equal.
  • When equals are subtracted from equals then, the remainder are equal.
  • Things that coincide with one another should be equal to each other.
  • The whole is greater than part.
  • Things that are double of the same things should be equal to one another.
  • Things that are halves of the same things should be equal to one another.

Therefore, 'If equals are added to equals, the wholes are unequal.' is the correct response.

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