
What is Idempotent law?
Answer
459.3k+ 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.
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