3) Determine if the proposition "Every set is an element of its power set" is true or false, and explain your answer.

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ISBN:9780470458365
Author:Erwin Kreyszig
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**Question 33:** Determine if the proposition "Every set is an element of its power set" is true or false, and explain your answer.

**Explanation:**

A power set of a set \( S \) consists of all possible subsets of \( S \), including the empty set and \( S \) itself as a subset. However, a set is not an element of its power set since the elements of a power set are subsets, not the set \( S \) itself. Therefore, the proposition is false.
Transcribed Image Text:**Question 33:** Determine if the proposition "Every set is an element of its power set" is true or false, and explain your answer. **Explanation:** A power set of a set \( S \) consists of all possible subsets of \( S \), including the empty set and \( S \) itself as a subset. However, a set is not an element of its power set since the elements of a power set are subsets, not the set \( S \) itself. Therefore, the proposition is false.
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