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Chapter 3: Problem 16

Use Euler diagrams to determine whether each argument is valid or invalid. All actors are artists. Sean Penn is an artist. Therefore, Sean Penn is an actor.

Short Answer

Expert verified
The argument is invalid.

Step by step solution

01

Draw the Diagram for the First Premise

The first premise states, 'All actors are artists'. To represent this, draw a circle labeled 'actors' inside a larger circle labeled 'artists'. This signifies that all actors are a subset of artists.
02

Incorporate the Second Premise Into the Diagram

The second premise is 'Sean Penn is an artist'. To illustrate this, place a dot inside the 'artists' circle (but not necessarily inside the 'actors' sub-circle) and label it 'Sean Penn'. This indicates that Sean Penn is part of the artists' group but it does not necessarily tell us if he is an actor or not.
03

Determine the Validity of the Conclusion

The conclusion is 'Sean Penn is an actor'. According to our diagram, Sean Penn is an artist. However, he's not necessarily an actor, even though all actors are artists. Therefore, the argument is invalid as the conclusion isn't necessarily true even though the premises are true.

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Most popular questions from this chapter

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If The Graduate and Midnight Cowboy are shown, then the performance is sold out. Midnight Cowboy was shown and the performance was not sold out. \(\therefore\) The Graduate was not shown.

Use Euler diagrams to determine whether each argument is valid or invalid. All professors are wise people. Some professors are actors. Therefore, some wise people are actors.

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If all electricity is off, then no lights work. Some lights work. Therefore, ...

Use Euler diagrams to determine whether each argument is valid or invalid. All professors are wise people. Some wise people are actors. Therefore, some professors are actors.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(p \wedge \sim q\) P____ \(\therefore \sim q\)
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