Consider the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B, if A CB then 8°CA. Use an element argument to construct a proof for the statement by putting selected sentences from the following scrambled list in the correct order. By definition of complement, xE B. Suppose A and B are any sets such that A C B, and suppose x E B". Suppose A and B are any sets such that A C B, and suppose x E B. Therefore, by definition of complement x € A°, and thus, by definition of subset, B c A°. If x were in A, then x would have to be in B by definition of subset. But xe B, and so x E A. Hence, x E A, because A NB = 0. Proof: 1. ---Select--- 2. ---Select- 3. -Select--- 4. -Select--- Need Help? Read It Submit Answer

Consider the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B, if A CB then 8°CA. Use an element argument to construct a proof for the statement by putting selected sentences from the following scrambled list in the correct order. By definition of complement, xE B. Suppose A and B are any sets such that A C B, and suppose x E B". Suppose A and B are any sets such that A C B, and suppose x E B. Therefore, by definition of complement x € A°, and thus, by definition of subset, B c A°. If x were in A, then x would have to be in B by definition of subset. But xe B, and so x E A. Hence, x E A, because A NB = 0. Proof: 1. ---Select--- 2. ---Select- 3. -Select--- 4. -Select--- Need Help? Read It Submit Answer

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the following statement. Assume that all sets are subsets of a universal set U.
For all sets A and B, if A CB then B° C AS.
Use an element argument to construct a proof for the statement by putting selected sentences from the following scrambled list in the correct order.
By definition of complement, x € B.
Suppose A and B are any sets such that A C B, and suppose x E BS.
Suppose A and B are any sets such that AC B, and suppose x E B.
Therefore, by definition of complement x E A°, and thus, by definition of subset, B° C A.
If x were in A, then x would have to be in B by definition of subset. But xe B, and so x E A.
Hence, x E A, because A NB = 0.
Proof:
1. ---Select-
2. ---Select---
3. ---Select--
-Select---
4.
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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---
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