CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Closure property does not hold good in integers for


A

multiplication

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

division

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

addition

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

subtraction

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

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.


flag
Suggest Corrections
thumbs-up
5
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Addition and Subtraction of Integers
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon