Table of Contents

- 1 Which operations integers are not closed?
- 2 Is multiplication closed for integers?
- 3 Are the integers closed?
- 4 Are integers closed under addition?
- 5 What is a closed operation?
- 6 Which operation does not hold closure property for integers?
- 7 What is an example of closed under multiplication?
- 8 What is closed under subtraction?

## Which operations integers are not closed?

Answer: The set of integers is not closed under the operation of division because when you divide one integer by another, you don’t always get another integer as the answer.

## Is multiplication closed for integers?

Answer: Integers and Natural numbers are the sets that are closed under multiplication.

**How do you know if an operation is closed?**

A set is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set. If the operation produces even one element outside of the set, the operation is not closed.

### Are the integers closed?

a) The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers. For example, 4 and 9 are both integers, but 4 ÷ 9 = 4/9. 4/9 is not an integer, so it is not in the set of integers!

### Are integers closed under addition?

For example, the set of even integers is closed under addition, but the set of odd integers is not. When a set S is not closed under some operations, one can usually find the smallest set containing S that is closed. This smallest closed set is called the closure of S (with respect to these operations).

**What are the 5 integer operations?**

We have four fundamental operations on integers. They are addition, subtraction, multiplication, and division.

#### What is a closed operation?

In mathematics, a set is closed under an operation if performing that operation on members of the set always produces a member of that set. For example, the positive integers are closed under addition, but not under subtraction: 1 − 2 is not a positive integer even though both 1 and 2 are positive integers.

#### Which operation does not hold closure property for integers?

division

Closure property does not hold in integers for division. Division of integers doesn’t follow the closure property since the quotient of any two integers a and b, may or may not be an integer.

**What sets are closed under subtraction?**

This smallest closed set is called the closure of S (with respect to these operations). For example, the closure under subtraction of the set of natural numbers, viewed as a subset of the real numbers, is the set of integers. An important example is that of topological closure.

## What is an example of closed under multiplication?

A set is “closed under (scalar) multiplication” if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.

## What is closed under subtraction?

so, closed under subtraction means if we subtract two numbers of a set than it must belong to that set. Integers: They are closed under subtraction. since, if we subtract two integers it will be an integer only. Irrational numbers: They are not closed under subtraction.

**What is closed set under addition?**

A set is “closed under addition” if the sum of any two members of the set also belongs to the set. For example, the set of even integers. Take any two even integers and add them together. The result is an even integer.