Some steps are missing from the following proof that for all sets (A B) C = (A C) (B C)
Chapter 6, Problem 29(choose chapter or problem)
Some steps are missing from the following proof that for all sets \((A \cup B)-C=(A-C) \cup(B-C)\). Indicate what they are, and then write the proof correctly.
Proof: Let A, B, and C be any sets. Then
\((A \cup B)-C=(A \cup B) \cap C^{c}\)
= \(\left(A \cap C^{c}\right) \cup\left(B \cap C^{c}\right)\)
= \((A-C) \cup(B-C)\)
Text Transcription:
(A cup B)-C=(A-C) cup(B-C)
(A cup B)-C=(A cup B) cap C^c
(A cap C^c) cup(B cap C^c)
(A-C) cup(B-C)
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