Math, asked by GautamPrabhu6733, 7 months ago

Is a commutative property associative property distributive property closure property

Answers

Answered by prithakundu
3

Step-by-step explanation:

  • commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, "3 − 5 ≠ 5 − 3"); such operations are not commutative, and so are referred to as noncommutative operations.

  • associative property

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like.

(a + b) + c = a + (b + c) – Yes, algebraic expressions are also associative for addition

  • distributive property

For example, in arithmetic:

2 ⋅ (1 + 3) = (2 ⋅ 1) + (2 ⋅ 3), but 2 / (1 + 3) ≠ (2 / 1) + (2 / 3).

On the left-hand side of the first equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the products added afterward. Because these give the same final answer (8), multiplication by 2 is said to distribute over the addition of 1 and 3. Since one could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, multiplication of real numbers distributes over addition of real numbers.

  • closure property

The closure property means that a set is closed for some mathematical operation. That is, a set is closed with respect to that operation if the operation can always be completed with elements in the set. Thus, a set either has or lacks closure with respect to a given operation.

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