Question

Closure property does not hold good in integers for

• A. multiplication
• B. division
• C. addition
• D. subtraction

Answer 1

The correct option is B

division

The explanation for the correct option:

Option B. Division

Define Closure Property:

Closure Property for a set of numbers states that when an arithmetic operation is performed on any two elements from the set, the result of the operation is always an element of that set. A set that follows Closure Property under a particular operation is said to be closed under that operation.

Examine Closure Property for the set of integers under division:

• When we divide an integer by another integer, the quotient may not always be an integer.
• For example when we divide $1$ by $2$, the quotient is a non-integer.
• Also, when the divisor is $0$, the quotient is undefined.
• Hence, Closure Property does not hold good in integers for division.

Hence, Option B is correct.

The explanation for the incorrect options:

Option A. Multiplication

• Since the product of any two integers is also an integer, hence Closure Property holds good in integers for Multiplication.
• For example $3$ multiplied by $2$ is $6$, which is an integer.

Hence, Option A is incorrect.

Option C. Addition

• Since the sum of any two integers is always an integer, hence Closure Property holds good for Addition of integers.
• For example the sum of the integers $3$ and $2$ is $5$, which is an integer.

Hence, Option C is incorrect.

Option D. Subtraction

• Since the difference of any two integers is also an integer, hence Closure Property holds good for Subtraction of integers.
• For example the difference of the integers $3$ and $2$ is $1$, which is again an integer.

Hence, Option D is incorrect.

Hence, the correct option is Option B.