The law a + b = b + a is calleda)Associative lawb)Distributive lawc)Closure lawd)Commutative lawCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Commutative law is the Law that says you can swap numbers around and still get the same answer when you add or when you multiply i.e a + b = b + a

Example:

You can swap when you add: 6 + 3 = 3 + 6 (= 9)

Answer

It is a law there is nothing to explain. u have to just mug it up and u can apply this in your questions. if we add and multiply by changing the postions of numbers we will get the same value. for example 2+3=3+2=5

Answer

Associative law

Answer

The law a b = b a is called the commutative law. This law states that the order of the elements does not matter when performing an operation. In other words, if we have two elements a and b, the commutative law states that a b will yield the same result as b a.

Explanation:

1. Commutative Law:
The commutative law is a fundamental property of addition and multiplication. It applies to both numbers and variables. The law states that the order of the elements does not affect the outcome of the operation.

For example, in addition:
a + b = b + a
This means that if we add a and b, it will give the same result as adding b and a.

Similarly, in multiplication:
a × b = b × a
This means that if we multiply a and b, it will give the same result as multiplying b and a.

2. Examples:
Let's consider a few examples to understand the commutative law further:

Example 1:
a = 2 and b = 3
Using the commutative law of addition:
2 + 3 = 3 + 2
5 = 5

Example 2:
a = x and b = y
Using the commutative law of multiplication:
x × y = y × x

3. Applications:
The commutative law is widely used in mathematics and various other fields. Some of its applications include:

- Algebra: The commutative law is used to simplify algebraic expressions and equations by rearranging terms.
- Arithmetic: It allows us to reorder numbers when performing addition or multiplication.
- Set theory: The commutative law is used to manipulate sets and perform operations such as union and intersection.
- Computer Science: It is employed in programming languages and algorithms to optimize calculations and improve efficiency.

In conclusion, the commutative law states that the order of elements does not affect the outcome of an operation. It is a fundamental property of addition and multiplication, and its applications extend to various fields of study.

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