Solved: Find the mistake in the following proof that for all sets A, B, and C, if A B
Chapter 6, Problem 20(choose chapter or problem)
Find the mistake in the following “proof” that for all sets A, B, and C, if \(A \subseteq B\) and \(B \subseteq C\) then \(A \subseteq C\).
“Proof: Suppose A, B, and C are sets such that \(A \subseteq B\) and \(B \subseteq C\). Since \(A \subseteq B\), there is an element x such that \(x \in A\) and \(x \in B\). Since \(B \subseteq C\), there is an element x such that \(x \in B\) and \(x \in C\). Hence there is an element x such that \(x \in A\) and \(x \in C\) and so \(A \subseteq C\).”
Text Transcription:
A subseteq B
B subseteq C
A subseteq C
A subseteq B
B subseteq C
A subseteq B
x in A
x in B
B subseteq C
x in A
x in B
x in A
x in C
A subseteq C
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