(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assign a grade of A (excellent) if the claim and proof are correct, even if the proof is not the simplest or the proof you would have given. Assign an F (failure) if the claim is incorrect, if the main idea of the proof is incorrect, or if most of the statements in it are incorrect. Assign a grade of C (partial credit) for a proof that is largely correct, but contains one or two incorrect statements or justifications. Whenever the proof is incorrect, explain your grade. Tell what is incorrect and why.

Claim: If A, B, and C are sets, and [tex] A \subseteq B [/tex] and [tex] B \subseteq C [/tex], then [tex] A \subseteq C [/tex].

Proof: Suppose x is any object. If [tex] x \in A [/tex], then [tex] x \in B [/tex], since [tex]A \subseteq B [/tex]. If [tex] x \in B [/tex], then [tex] x \in C [/tex], since [tex] B \subseteq C [/tex]. Therefore [tex] x \in C [/tex]. Therefore [tex] A \subseteq C [/tex].

3. The attempt at a solution

Am I correct in wanting to give this proof a grade of an A, even if the language seems a bit shaky?

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# Homework Help: Proof to Grade

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