Question

#2: answer the following. your response must be in your own words.

create your own example of equivalent sets. how are equivalent sets different from equal sets?

Explanation:

Define equivalent sets with an example

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Define equal sets with an example

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Distinguish equivalent sets from equal sets

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Answer:

Example of Equivalent Sets:
Let Set \(A = \{1, 2, 3\}\) and Set \(B = \{\text{red}, \text{blue}, \text{green}\}\).
These sets are equivalent because they contain the exact same number of elements (their cardinality is equal, \(n(A) = n(B) = 3\)), allowing a one-to-one correspondence between them.

Difference between Equivalent and Equal Sets:

• Equivalent sets only require having the same number of elements (same cardinality), regardless of what those elements actually are.
• Equal sets must contain the exact same elements, regardless of their order (for example, \(\{1, 2, 3\}\) and \(\{3, 2, 1\}\)). Equal sets are always equivalent, but equivalent sets are not necessarily equal.