Question

Things which are three times the same thing are:
A) Equal to each other
B) not equal to each other
C) half of the same
D) double of the same thing

Answer 1

Hint:
We will assume the thing to be some variables. We will make linear equations according to the data given in the question. We will compare these equations and find the correct option.

Complete step by step solution:
We know that there are some things that are three times the same thing. We will assume that the first thing is represented by variable \[x\], the second thing is represented by variable \[y\], the third thing is represented by variable \[z\] and so on. We will assume that this same thing is represented by the variable \[a\].
So, according to the question; the first thing will be equal to \[3a\], the second thing will also be equal to \[3a\] and so on…
\[ \Rightarrow x = 3a\]……..\[\left( 1 \right)\]
\[ \Rightarrow y = 3a\]……..\[\left( 2 \right)\]
\[ \Rightarrow z = 3a\]………\[\left( 3 \right)\]
\[\begin{array}{l}.\\.\\.\end{array}\]
We will compare the first and the second equation:
\[ \Rightarrow x = 3a = y\] …………\[\left( 4 \right)\]
We can see from the fourth equation that:
\[ \Rightarrow x = y\]………….\[\left( 5 \right)\]
We will compare the second and the third equation:
\[ \Rightarrow y = 3a = z\]………..\[\left( 6 \right)\]
We can see from the sixth equation that:
\[ \Rightarrow y = z\]…………\[\left( 7 \right)\]
We will compare the fifth and the seventh equation:
\[ \Rightarrow x = y\]
\[ \Rightarrow y = z\]
\[ \Rightarrow x = y = z\]………..\[\left( 8 \right)\]
We can observe from the eighth equation that all the things are equal.

$\therefore $ Option A is the correct option.

Note:
We can also solve this question using Euclid’s Axioms.
We know that there are some things that are three times the same thing. We will assume that the first thing is represented by variable \[x\], the second thing is represented by variable \[y\], the third thing is represented by variable \[z\] and so on. We will assume that this same thing is represented by the variable \[a\].
So, according to the question; the first thing will be equal to \[3a\], the second thing will also be equal to \[3a\] and so on…
\[x = 3a\]………\[\left( 1 \right)\]
\[y = 3a\]………\[\left( 2 \right)\]
\[z = 3a\]………\[\left( 3 \right)\]
\[\begin{array}{l}.\\.\\.\end{array}\]
We know that according to Euclid’s first axiom; things that are equal to the same thing are also equal to each other. So, we can conclude from the first, second and third equation that:
\[ \Rightarrow x = y = z\]
$\therefore $ Things which are three times the same thing are equal to each other.
Option A is the correct option.