Question

According to Euclid: The whole is greater than the part .State whether that this is true or false.
$\left( A \right).$ True
$\left( B \right).$ False

Answer 1

Hint: This problem is based on the Euclid’s axiom. Let us consider three numbers $A,B$ and $C$ and let us take the sum of $A$ and $B$ as $C$ $($ $C = A + B$$)$ and prove that $C$ is greater than $A$ and $B$ individually $($ $C > A$ and $C > B$ $)$ and hence whole is greater than the part

Complete answer:
Consider the three numbers $A,B$ and $C$
Let us consider,
 $ \Rightarrow C = A + B$ ……..$\left( 1 \right)$
For example, $A = 4$ and $B = 6$ …….$\left( 2 \right)$
From equation \[\left( 1 \right)\]
$ \Rightarrow C = 6 + 4$
Therefore, $C = 10$ ………$\left( 3 \right)$
Hence, from equation $\left( 3 \right)$ it is seen that the sum that $C = 10$ is greater that both the number that is $A$ and $B$ that is $4$ and $6$ respectively.
Therefore, the whole is greater than the part
Hence the given statement is true.

Note:
Similarly, the things which are equal to the same are said to be equal to one another, suppose equals are added to equal the result will be equal i.e., in general \[a + b = c\]. Suppose equals are subtracted to equal the result will be equal i.e., in general \[a - b = c\] the things which coincide with one another are equal to one another. Here a and b can be any numbers. The things which are halves of the same things are always equal to one another and also the things which are double of the same things are always equal to one another. For example: \[1 = 2 \times \dfrac{1}{2}\].