Chapter 6.4, Problem 1TY

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Chapter
Section

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In the comparison between the structure of the set of statement forms and the set of subsets of a universal set, the or operatioln V corresponds to --------, the and operation ? corresponds to -----, a tautology t corresponds to -------- a contradiction c corresponds to ----------, and the negation operation, denoted ?, corresponds to -------

To determine

To fill in the blanks of the given statement.

In the comparison between the structure of the set of statement forms and the set of subsets of a universal set, the or operation corresponds to theoperationofunion, the and operation corresponds to theoperationofintersection, a tautology t corresponds to auniversalsetU, a contradiction c corresponds to theemptyset and the negation operation, denoted , corresponds to theoperationofcomplementation,denotedbyusingthesuperscriptc.

Explanation

Given:

The given statement is “In the comparison between the structure of the set of statement forms and the set of subsets of a universal set, the or operation corresponds to ______, the and operation corresponds to a tautology t corresponds to, a contradiction c corresponds toand the negation operation, denoted , corresponds to.”

The logical equivalences of set operations are as shown below.

For theoperationofunion, the logical equivalence is the or operation .

For theoperationofintersection, the logical equivalence isthe and operation .

For auniversalsetU, the logical equivalence isa tautology t.

For theemptyset, the logical equivalence isa contradiction c.

And for the operation of complementation, the logical equivalence is the negation operation.

Hence, In the comparison between the structure of the set of statement forms and the set of subsets of a universal set, the or operation corresponds to theoperationofunion, the and operation corresponds to theoperationofintersection, a tautology t corresponds to auniversalsetU, a contradiction c corresponds to theemptyset and the negation operation, denoted , corresponds to theoperationofcomplementation,denotedbyusingthesuperscriptc.

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