Sets Definitions and Examples
Explain and give examples for the following:
- Equivalent sets vs. Equal sets
- Cardinality of sets and how cardinality relates to the number of subsets of a set
- Subset vs. Proper Subset
- Complement of a set vs. Complement of a universal set.
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Solution Preview
- Equivalent sets vs. Equal sets
Answer: First, we need to know the difference between equivalent sets and equal sets. Equivalent sets are sets which have the same number of elements, but the entries of the set are different. However, equal sets are sets which have both the same number of elements, and the exact same entries.
For example, the sets {2, 4, 6} and {1, 3, 5} are equivalent sets but not equal sets. They both have 3 elements but the entries are different.
The sets {1, 3, 5} and {5, 3, 1} are equal because they both have 3 elements with the same entries.
- Cardinality of sets and ...
Solution Summary
This solution explains the differences between: equivalent sets vs. equal sets, subset vs. proper subset, and complement of a set vs. complement of a universal set; it also explains the concept of 'cardinality of sets' and the relation between cardinality and the number of subsets of a set.