Question

If, A: Every whole number is a natural number R : 0 is not a natural number.
Then which of the following statements is true?
A) A is false and R is the correct explanation of A.
B) A is true and R is the correct explanation of A.
C) A is true and R is false.
D) Both A and R are true.

Answer 1

Hint:
In this problem, we will be using the definition of natural and whole numbers. Natural numbers are a part of the number system which includes all the positive integers from 1 to infinity. It is an integer which is always greater than 0. Whole numbers are included in the number system which contains all the positive integers from 0 to infinity.

Complete step by step solution:
Complete step-by-step solution:
Now, the natural number contains all positive integers starting from one to infinity.
Natural numbers start from 1, 2, 3, 4, 5, 6, 7, 8, ……………. and go on.
Now, whole numbers contain all positive integers starting from zero to infinity.
Whole number starts from 0, 1, 2, 3, 4, 5, 6, 7, 8, ……………… and go on.
We can see zero is the whole number but not the natural number.
By observing the above statement, we can say that a natural number will contain all the whole numbers except zero. Therefore, natural numbers cannot contain all whole numbers.
It is a false statement that every whole number is a natural number but it is a correct statement that zero is not a natural number.

So, the option (A) is the correct option.

Note:
In such questions, we need to follow the basic definition of natural and whole numbers and write the range of natural and whole numbers as we have written above then try to observe the all numbers of natural numbers and whole numbers. In this way, we would be able to easily identify natural numbers that cannot contain inside the range of whole numbers.