NAME
CCR 3
MAT 300 · FALL 2014
Critique and correct the following proof, as if you were grading someone’s homework in
great detail. (Write directly on this sheet.) Also provide a revised version of the proof;
your revision should use the basic idea of the original proof (if possible), but should be an
improvement in terms of reasoning and exposition. (Write your proof on the back of this
sheet.)
Theorem. Suppose A, B, and C are sets, with A ∩ C ⊆ B. If a ∈ C, then
a∈
/ A \ B.
I would like to use proof by contradiction. assume
1
Proof.
2
a ∈ C and also a ∈ B \ A. This means that a ∈ C and
3
a ∈ B and a ∈
/ A. Thus a ∈
/ A \ B, because A \ B ⊆ A.
4
This is a contradiction, so I must have a ∈
/ A \ B.
Date: September 11, 2014. Due Date: Wednesday, September 24, 2014.
S. Kaliszewski, School of Mathematical and Statistical Sciences, Arizona State University.