Question

Write the generalized form of closure property under division

Answer 1

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The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division i.e., a ÷ b is not always a whole number. From the property, we have, 14 ÷ 7 = 2 (whole number) but 7 ÷ 14 = ½ (not a whole number).

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Answer 2

Answer:

Properties of Sets Under an Operation

Mathematicians are often interested in whether or not certain sets have particular properties under a given operation. One reason that mathematicians were interested in this was so that they could determine when equations would have solutions. If a set under a given operation has certain general properties, then we can solve linear equations in that set, for example.

There are several important properties that a set may or may not satisfy under a particular operation. A property is a certain rule that holds if it is true for all elements of a set under the given operation and a property does not hold if there is at least one pair of elements that do not follow the property under the given operation.

Talking about properties in this abstract way doesn't really make any sense yet, so let’s look at some examples of properties so that you can better understand what they are. In this lecture, we will learn about the closure property.

The Property of Closure

A set has the closure property under a particular operation if the result of the operation is always an element in the set. If a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”