The homework for Unit 2 Logic and Proof is an important part of learning the course and understanding the concepts. Homework 6 is no exception, and it is important for students to understand the question, the answers, and the reasoning behind the answers. This article will serve as a comprehensive guide for Homework 6 so that students can understand the concepts and get the most out of their learning experience.

## The Question

Homework 6 asks students to prove the following statement using the contrapositive method: If a set contains more than one element, then the set is not a singleton set. The contrapositive method is a type of proof that starts with the form: If not P then not Q. In this case, the statement reads: If a set is a singleton set, then the set contains only one element.

## The Answer

To prove this statement, the contrapositive method should be used. To start, the statement should be rewritten in the form: If not P then not Q. In this case, this statement reads: If a set is not a singleton set, then the set contains more than one element. To prove this statement, students should assume that the set contains more than one element and then show that the set cannot be a singleton set.

To do this, students should show that a singleton set is defined as a set containing only one element. Since the set in question contains more than one element, it is not a singleton set. Therefore, it follows that if a set contains more than one element, then the set is not a singleton set.

## The Reasoning

The reasoning behind this proof is fairly straightforward. A singleton set is defined as a set that contains only one element. If a set contains more than one element, then it is not a singleton set. Therefore, if a set contains more than one element, then the set is not a singleton set.

## Conclusion

Homework 6 of Unit 2 Logic and Proof requires students to prove a statement using the contrapositive method. This statement reads: If a set contains more than one element, then the set is not a singleton set. This can be proven by assuming that the set contains more than one element and then showing that a singleton set is defined as a set containing only one element, so the set in question cannot be a singleton set. This guide has provided an explanation of the question, the answer, and the reasoning behind the answer so that students can understand the concept and get the most out of their learning experience.

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