Consider the following statement. If U denotes a universal set, then UC = 0. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set. Let U be a universal set and suppose UC + Ø. So, by definition of complement x E U. Thus x EU and x € U, which is a contradiction. Then there exists an element x in UC. But, by definition of a universal set, U contains all elements under discussion, and so x E U. Let U be a universal set and suppose UC- 0. So, by definition of complement x € U. But, by definition of a universal set, UC contains no elements. Proof by contradiction: Select-- Select- Select 4.--Select- 5. -Select 6. Hence the supposition is false, and so UC = 0.
Consider the following statement. If U denotes a universal set, then UC = 0. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set. Let U be a universal set and suppose UC + Ø. So, by definition of complement x E U. Thus x EU and x € U, which is a contradiction. Then there exists an element x in UC. But, by definition of a universal set, U contains all elements under discussion, and so x E U. Let U be a universal set and suppose UC- 0. So, by definition of complement x € U. But, by definition of a universal set, UC contains no elements. Proof by contradiction: Select-- Select- Select 4.--Select- 5. -Select 6. Hence the supposition is false, and so UC = 0.
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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Transcribed Image Text:Consider the following statement.
If U denotes a universal set, then UC = 0.
Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set.
Let U be a universal set and suppose UC + Ø.
So, by definition of complement x EU.
Thus x EU and x € U, which is a contradiction.
Then there exists an element x in UC.
But, by definition of a universal set, U contains all elements under discussion, and so x E U.
Let U be a universal set and suppose UC - 0.
So, by definition of complement x ¢ U.
But, by definition of a universal set, UC contains no elements.
Proof by contradiction:
Select--
2
Select-
Select
4.
--Select-
5. -Select
6. Hence the supposition is false, and so UC = 0.
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