Question

Integers is not closed under -
(A) Addition
(B) Subtraction
(C) Multiplication
(D) None of these

Answer 1

Hint :- Integers :- Make use of the definition of integers which says that includes all the negative and non negative whole numbers but not decimals
\[\infty \] ............. -3 -2 -1 0 1 2 3 4............. \[\infty \]


Complete step by step solution
The integers closed under addition, multiplication and subtraction, but not under division because
when you divide one integer by another, you don’t always get another integer.
For example :- \[{\text{4}}\]and \[{\text{9}}\] both are integers, but \[{\text{4}} \div {\text{9 }} = \dfrac{4}{9}\] is not an integer.
Step – I
If we take any two integers, we multiply those integers; the result is also an integer. Hence, we can say that integers are closed under multiplication.
\[3 \times 6 - = 18 - \]integer
Step – II
You had also seen the operation of addition so it we add
For example :- addition
\[{\text{3}} + {\text{2 }} = {\text{ 5}}\]
Step – III
You had also seen the operation of subtraction so it we subtract
\[{\text{5 }} - {\text{ 2 }} = {\text{ 3}}\]
So (D) None of these is the right answer.

Note: In this question we were asked about integers;in case if the condition has been asked for any other set of numbers,(Real numbers,rational etc…)then solve it according to the condition given and give the answer.