Question

Which of the following statements is incorrect?
A. Whole numbers are closed under addition
B. Whole numbers are closed under multiplication
C. Whole numbers are closed under subtraction
D. Whole numbers are not closed under subtraction

Answer 1

Hint: To solve this question first we need to recall the definition of closure property and conditions when a set to be closed under any operation. Then one by one we will analyze options to find which one is incorrect.

Complete step by step answer:
Let us take option A- Whole numbers are closed under addition
For a whole number, the closure property says that if we add two whole numbers then the result will always be a whole number. For example $ 2+3=5 $ .
Here, $ 2,3\And 5 $ are whole numbers. So, Whole numbers are closed under addition. Hence this statement is correct.
Now, let us take option B- Whole numbers are closed under multiplication
The closure property of multiplication says that if we multiply two whole numbers we get a whole number in the product. For example $30\times 2=60 $
Here, $ 30,2\And 60 $ are whole numbers. So, Whole numbers are closed under multiplication. Hence this statement is correct.
Now, let us take option C- Whole numbers are closed under subtraction
The closure property of whole numbers tells that when two whole numbers are subtracted the resultant may not always be a whole number. For example- $ 2-3=-1 $
Here $ -1 $ is not a whole number. So, Whole numbers are not closed under subtraction. Hence this statement is incorrect and option D is correct.
Hence we get that only option C is an incorrect statement.

Note:
The key point to solve this type of question is to analyze the options one by one and reach the conclusion. Always take an example to understand the statements.