the wing tatemer Assume that all sets are subsets of a universal set U. For all sets A and B, if A CB then BC C AC. n element argument to construct a proof for the statement by putting selected sentences from the following sc Therefore, by definition of complement x E Aº, and thus, by definition of subset, BC C AC. Hence, x € A, because A N B = Ø. By definition of complement, x € B. Suppose A and B are any sets such that A C B, and suppose x E Bº. If x were in A, then x would have to be in B by definition of subset. But x € B, and so x€A. Suppose A and B are any sets such that A S B. and suppose x E B.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the following statement. Assume that all sets are subsets of a universal set U.
For all sets A and B, if A C B then B C A°.
Use an element argument to construct a proof for the statement by putting selected sentences from the following scrambled list in the correct order.
Therefore, by definition of complement x E A, and thus, by definition of subset, B CA.
Hence, x € A, because A NB = 0.
By definition of complement, x € B.
Suppose A and B are any sets such that AC B, and suppose x E B.
If x were in A, then x would have to be in B by definition of subset. But x B, and so x A.
Suppose A and B are any sets such that A C B, and suppose x E B.
Proof:
1.
.--Select---
2.---Select---
3. --Select---
4. |--Select---
Transcribed Image Text:Consider the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B, if A C B then B C A°. Use an element argument to construct a proof for the statement by putting selected sentences from the following scrambled list in the correct order. Therefore, by definition of complement x E A, and thus, by definition of subset, B CA. Hence, x € A, because A NB = 0. By definition of complement, x € B. Suppose A and B are any sets such that AC B, and suppose x E B. If x were in A, then x would have to be in B by definition of subset. But x B, and so x A. Suppose A and B are any sets such that A C B, and suppose x E B. Proof: 1. .--Select--- 2.---Select--- 3. --Select--- 4. |--Select---
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