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Chapter 9: Problem 14

Are the elements of a set ordered or unordered?

Short Answer

Expert verified
Explain your answer briefly. Answer: The elements in a set are unordered. This means that the arrangement of the elements does not matter, and two sets are considered equal if they have the same elements, regardless of the order in which they are listed.

Step by step solution

01

Definition of a Set

A set is a collection of distinct objects, called elements. Sets are usually denoted by capital letters, while elements are denoted by lowercase letters. A set can be written explicitly by listing its elements, enclosed in curly brackets. For example, A = {a, b, c}.
02

Ordered vs. Unordered Elements

The elements in a set are unordered, which means that the arrangement of the elements does not matter. In other words, a set with elements {a, b, c} is equal to a set with elements {c, b, a} or any other arrangement of these elements because the order of the elements does not have any significance in a set.
03

Comparing Sets

When comparing sets, only the presence or absence of elements matters, not their order. For example, if set A has the elements {1, 2, 3}, and set B has the elements {3, 1, 2}, we would consider A and B to be equal sets ({A} = {B}) because they have the same elements, even though they are listed in a different order.
04

Conclusion

The elements of a set are unordered. The order in which they are listed does not change the set, and two sets are considered equal if they have the same elements, regardless of the order in which they are listed.

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Most popular questions from this chapter

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After the following code executes, what elements will be members of set3? $$\begin{array}{l}\text { set1 }=\operatorname{set}\left(\left[' a^{\prime}, \quad^{\prime} b^{\prime},\quad^{\prime}c^{\prime}\right]\right) \\ \text { set } 2=\operatorname{set}\left(\left[' b^{\prime}, \quad^{\prime} c^{\prime}, \quad^{\prime} d^{\prime}\right]\right) \\\\\text { set } 3=\text { set1. symmetric }_{-} \text {difference (set2) }\end{array}$$

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After the following code executes, what elements will be members of set3? \\[\begin{array}{l}\text { set1 }=\operatorname{set}([1,2,3,4]) \\ \text { set } 2=\operatorname{set}([3,4,5,6]) \\ \text { set } 3=\text { set } 1 . \text { intersection (set2) }\end{array}\\]
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