
What is Idempotent law?
Answer
464.7k+ views
Hint: Idempotent can be said to be an operation which can be repeated again without changing the result. That is, the expression where comes in the domain of and comes as a reference for the law. So, regardless of the number of the operations done, the expression will always yield the same result.
Complete step-by-step solution:
According to the given question, we have to explain the idempotent law.
The term idempotent would mean the repetition of a single work and still getting the same result. The law is useful both in mathematics as well as in computers for Boolean algebra.
Idempotent law can be expressed as , where can be any operation.
In mathematics, we use idempotent law in laws of sets, let’s take a look how it is used in the union of sets as well as the intersection of sets.
1) Union set –
In union sets, we take all the elements present in both the sets involved in union operation.
Let A be a set having elements 1, 2 and 3, that is,
If we take the union of A with A, we will get the same set as the elements are the same.
So, we have,
2) Intersection set -
In intersection sets, we take only the common elements present in both the sets involved in union operation.
Let A be a set having elements 1, 2 and 3, that is,
If we take the intersection of set A with set A, we will get the same set as the elements are the same.
So, we have,
Note: The only idempotent element number are 1 and 0 in the multiplication operation as they give 1 and 0 respectively when multiplied by itself, that is,
And no other number holds the idempotent law true.
Complete step-by-step solution:
According to the given question, we have to explain the idempotent law.
The term idempotent would mean the repetition of a single work and still getting the same result. The law is useful both in mathematics as well as in computers for Boolean algebra.
Idempotent law can be expressed as
In mathematics, we use idempotent law in laws of sets, let’s take a look how it is used in the union of sets as well as the intersection of sets.
1) Union set –
In union sets, we take all the elements present in both the sets involved in union operation.
Let A be a set having elements 1, 2 and 3, that is,
If we take the union of A with A, we will get the same set as the elements are the same.
So, we have,
2) Intersection set -
In intersection sets, we take only the common elements present in both the sets involved in union operation.
Let A be a set having elements 1, 2 and 3, that is,
If we take the intersection of set A with set A, we will get the same set as the elements are the same.
So, we have,
Note: The only idempotent element number are 1 and 0 in the multiplication operation as they give 1 and 0 respectively when multiplied by itself, that is,
And no other number holds the idempotent law true.
Latest Vedantu courses for you
Grade 8 | CBSE | SCHOOL | English
Vedantu 8 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹45,300 per year
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Trending doubts
The flightless birds Rhea Kiwi and Emu respectively class 11 biology CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

A car travels 100 km at a speed of 60 kmh and returns class 11 physics CBSE

What is 1s 2s 2p 3s 3p class 11 chemistry CBSE

In tea plantations and hedge making gardeners trim class 11 biology CBSE

What is the type of food and mode of feeding of the class 11 biology CBSE
