Question

Choose the correct option or options from the given options below by solving the following question:
Which of the following is NOT true?
A. Every whole number has a successor.
B. Every whole number has a predecessor.
C. \[0\] is the least whole number.
D. Every natural number is a whole number.

Answer 1

Hint: Consider every statement given in the options and verify if they are true or not. Considering they are about whole numbers, define the whole numbers and write their properties and validate if the given statements match them.

Complete step-by-step solution:
The first statement given is:
Every whole number has a successor.
Successor means the number which comes by adding \[1\] to the present number. We have the smallest whole number as \[0\]. If we add \[1\] to \[0\], we get;
\[0 + 1 = 1\].
Since \[1\] is also a whole number, we can say that every whole number has a successor. Therefore, option A is true.
The second statement given is:
Every whole number has a predecessor.
Predecessor means the number which comes by subtracting \[1\] to the present number. We have the smallest whole number as \[0\]. If we subtract \[1\] from \[0\], we get;
\[0 - 1 = - 1\]
Since \[ - 1\] is not a whole number, we can say that every whole number does not have a predecessor. Therefore, option B is false.
The third statement given is:
\[0\]is the least whole number.
Option C is true because \[0\] is the smallest whole number. The whole numbers start from \[0\].
The fourth statement given is:
Every natural number is a whole number.
Natural numbers start from \[1\] whereas the whole numbers start from \[0\]. Every natural number is a whole number because there is a union of whole numbers and natural numbers after \[0\].
Therefore, option D is true.

The true statements are A, C and D.

Note: In mathematical inception, natural numbers are those which are used in contributing a value and counting in a practical world which starts from one and continues till infinity. Whereas whole numbers are those which also consist of a null value that is zero as a single number which does not contribute to anything.