Part 2: Proof that P(A) n P(B) s P(AN B).To prove part 2, select options from the list and put them in the correct order.StatementExplanationSuppose A and B are any sets.1. Let X be any element in ---Select---Select-2. --Select--for every x in X, xE A and xe Bfor every x in X, xE ANBThen Xe P(A) and Xe P(B)P(ANB)Then XANBP(A) N P(B)Hence, XA and XB---Select-3. -Select-----Select-4. So,-Select------Select-5. Thus,Select---Select---6. ---Select-----Select-7. Therefore, XeSelect---Select---8. Since X could be any element in --Select-| it follows that every element in -Select---is in --Select---9. Therefore, P(A) n P(8) S P(AN B).Need Help?Read ItSubmit Answer Prove the following statement. Assume that all sets are subsets of a universal set U.For all sets A and B, P(AN B) = P(A) N P(B).Proof: Consider the options in the following scrambled list.for every x in X, x E A and xeBfor every x in X, x E ANBThen XE P(A) and Xe P(8)P(AN B)Then XCANBP(A) n P(B)Hence, XEA and XEBby definition of intersectionby definition of power setby definition of subsetPart 1: Proof that P(AN B) S P(A) N P(B).To prove part 1, select options from the list and put them in the correct order.StatementExplanationSuppose A and B are any sets.1. Let X be any element in -Select-2. ---Select-----Select-3. So,-Select------Select-4. Thus, -Select----Select-5. --Select---Select-6. ---Select-----Select--7. Therefore, X E --Select-----Select-8. Since X could be any element in --Select--v it follows that every element in -Select---v is in --Select--

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Answered: Prove the following statement. Assume…

Prove the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B, P(AN B) = P(A) n P(8).

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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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Part 2: Proof that P(A) n P(B) s P(AN B).
To prove part 2, select options from the list and put them in the correct order.
Statement
Explanation
Suppose A and B are any sets.
1. Let X be any element in ---Select--
-Select-
2. --Select--
for every x in X, xE A and xe B
for every x in X, xE ANB
Then Xe P(A) and Xe P(B)
P(ANB)
Then XANB
P(A) N P(B)
Hence, XA and XB
---Select-
3. -Select--
---Select-
4. So,
-Select---
---Select-
5. Thus,
Select--
-Select---
6. ---Select--
---Select-
7. Therefore, Xe
Select--
-Select---
8. Since X could be any element in --Select-
| it follows that every element in -Select---
is in --Select---
9. Therefore, P(A) n P(8) S P(AN B).
Need Help?
Read It
Submit Answer

Prove the following statement. Assume that all sets are subsets of a universal set U.
For all sets A and B, P(AN B) = P(A) N P(B).
Proof: Consider the options in the following scrambled list.
for every x in X, x E A and xeB
for every x in X, x E ANB
Then XE P(A) and Xe P(8)
P(AN B)
Then XCANB
P(A) n P(B)
Hence, XEA and XEB
by definition of intersection
by definition of power set
by definition of subset
Part 1: Proof that P(AN B) S P(A) N P(B).
To prove part 1, select options from the list and put them in the correct order.
Statement
Explanation
Suppose A and B are any sets.
1. Let X be any element in -Select-
2. ---Select--
---Select-
3. So,
-Select---
---Select-
4. Thus, -Select-
---Select-
5. --Select--
-Select-
6. ---Select--
---Select--
7. Therefore, X E --Select--
---Select-
8. Since X could be any element in --Select--
v it follows that every element in -Select---
v is in --Select--

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