Chapter 1.1, Problem 53E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In Exercises 51 to 54, use Venn diagrams to determine whether the argument is valid or not valid.*

1) All Boy Scouts serve the United States of America.

2) Sean serves the United States of America.

C) Sean is a Boy Scout.

To determine

Whether the argument is valid or not using Venn diagram.

Explanation

**Approach:**

Venn diagram:

When a Venn diagram is used to represent the statement “If *P*, then *Q*”, circle *P* lies in circle *Q*; that is, *P* is the subset of *Q*.

Using a Venn diagram, the statement “If *P*, then *Q*” is represented by the following diagram:

The statement “If *P*, then *Q*” is sometimes expressed in the form “All *P* are *Q*”

**Procedure:**

The given statement is “All Boy Scouts serve the United States of America.”

This statement is of the form “All *P* are *Q*”. Let’s express this statement in the form of “If *P*, then *Q*”

So, the first statement can be written as “If a person is a Boy Scout, then he serves the United States of America...

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