I do not undeerstand this question for homework.
Determine if the set is closed for the given operation.
1. yes or no- The set of positive fractions for division.
2. yes or no=The set of positive integers for subtraction.
Can someone help me?
Of course, I can help you understand how to determine if a set is closed for a given operation.
To determine if a set is closed under a particular operation, you need to check if performing that operation on any elements of the set will always result in another element that is also in the set.
Let's apply this concept to the given sets and operations:
1. The set of positive fractions for division:
To check if this set is closed for division, we need to divide any two positive fractions and see if the result is also a positive fraction. For example, let's take two positive fractions, 3/2 and 4/5:
(3/2) ÷ (4/5) = (3/2) × (5/4) = 15/8
The result, 15/8, is still a positive fraction, so it is a part of the original set. Therefore, the set of positive fractions is closed under division.
2. The set of positive integers for subtraction:
Similarly, to check if this set is closed for subtraction, we need to subtract any two positive integers and see if the result is also a positive integer. For example, let's take two positive integers, 7 and 3:
7 - 3 = 4
The result, 4, is still a positive integer, so it is a part of the original set. Therefore, the set of positive integers is closed under subtraction.
In conclusion:
1. The set of positive fractions for division is closed under division (yes).
2. The set of positive integers for subtraction is closed under subtraction (yes).
I hope this explanation helps you understand how to determine if a set is closed for a given operation. If you have any further questions, feel free to ask!