4. It is known that if x = 2z and y = 2z, then x = y. Then Euclid's axiom that
illustrates the statement is:
(a) Second axiom
(b) fourth axiom
(c) sixth axiom
(d) seventh axiom
Answers
Given : It is known that if x = 2z and y = 2z, then x = y
(1) Things which are equal to the same thing are equal to one another.
(2) If equals are added to equals, the wholes are equal.
(3) If equals are subtracted from equals, the remainders are equal.
(4) Things which coincide with one another are equal to one another.
(5) The whole is greater than the part.
(6) Things which are double of the same things are equal to one another.
(7) Things which are halves of the same things are equal to one another
To Find : Euclid's axiom that illustrates the statement
(a) Second axiom
(b) fourth axiom
(c) sixth axiom
(d) seventh axiom
Solution:
x = 2z ( x is double of z)
y = 2z, (y is double of z)
then x = y ( they are equal to each other )
(6) Things which are double of the same things are equal to one another.
in given options sixth axiom illustrates the statement
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Answer:
things which are equal to the same thing are equal to one another