Question

Write all properties:-
1. Closure property
2. Associative property
3. Commutative property
4. Distributive property.

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Answer 1

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Closure Property : A set that is closed under an operation or collection of operations is said to satisfy a closure property.

Associative property : In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.

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.

Distributive Property : In mathematics, the distributive property of binary operations generalizes the distributive law from Boolean algebra and elementary algebra. In propositional logic, distribution refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and disjunctions within logical proofs.

Answer 2

Answer:

Associative property:- According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped. Here's an example of how the sum does NOT change irrespective of how the addends are grouped. Here's another example.

Commutative property:- We learned that the commutative property of addition tells us numbers can be added in any order and you will still get the same answer. The formula for this property is a + b = b + a. For example, adding 1 + 2 or 2 + 1 will give us the same answer according to the commutative property of addition.

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.

Distributive property:- To “distribute”

means to divide something or give share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.