Valid Arguments

Valid Argument Definition

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volume_mute

A propositional wff of the form \(P_1∧P_2∧...∧P_n→Q\) is a valid argument under what condition?

It has at least one true hypothesis.

It is a tautology.

It has a true conclusion.

It is a contradiction.

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Explanation

Hypotheses and Conclusion

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In the symbolic form \(P_1∧P_2∧...∧P_n→Q\), what are \(P_1,...,P_n\) called?

Tautologies

Conclusions

Derivation rules

Hypotheses

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Explanation

Logical Conclusion

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volume_mute

When is \(Q\) a logical conclusion from \(P_1,...,P_n\)?

Whenever \(Q\) is unrelated to the hypotheses.

Whenever \(Q\) is true in every interpretation.

Whenever the truth of \(P_1,...,P_n\) implies the truth of \(Q\).

Whenever all hypotheses are false.

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Explanation

Incidental True Conclusion

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volume_mute

Why is an argument not valid merely because its hypotheses and conclusion are all true?

A valid argument cannot have true hypotheses.

A valid argument requires exactly one hypothesis.

A valid argument requires all statements to be false.

The conclusion may be an isolated true fact not related to the hypotheses.

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Explanation

Proof Sequence Definition

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volume_mute

What is a proof sequence?

A list of all possible conclusions.

A truth table for every hypothesis.

A set of unrelated true statements.

A sequence of wffs in which each wff is either a hypothesis or the result of applying a derivation rule to earlier wffs.

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Explanation

Correct Formal System

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volume_mute

What does it mean for a formal system to be correct?

Every valid argument should be provable.

Only valid arguments should be provable.

No arguments should be provable.

Every argument should be provable.

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Explanation

Complete Formal System

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volume_mute

What does it mean for a formal system to be complete?

Every valid argument should be provable.

Only valid arguments should be provable.

Every hypothesis must be false.

Every proof sequence must end with a hypothesis.

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Explanation

Modus Ponens Form

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volume_mute

The wff \((A→B)∧A→B\) is an example of which argument form?

Modus tollens

Simplification

Addition

Modus ponens

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Explanation

Modus Ponens Rule

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volume_mute

What does modus ponens allow?

From \(P\) and \(P→Q\), derive \(Q\).

From \(P∧Q\), derive \(P\).

From \(P\) and \(Q\), derive \(P∧Q\).

From \(P→Q\) and \(Q'\), derive \(P'\).

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Explanation

Equivalent Descriptions

2 pts

volume_mute

Which phrases describe the same idea as \(Q\) is a logical conclusion from \(P_1,...,P_n\)? Select all that apply.

\(P_1,...,P_n\) logically imply \(Q\).

\(Q\) is true for all possible worlds.

\(Q\) follows logically from \(P_1,...,P_n\).

\(Q\) can be logically deduced from \(P_1,...,P_n\).

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Explanation

Formal System Goals

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What properties are desired for a formal logic system? Select all that apply.

Completeness

A minimum set of derivation rules

A maximum set of derivation rules

Correctness

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Valid Argument Definition

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Explanation

Hypotheses and Conclusion

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Explanation

Logical Conclusion

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Explanation

Incidental True Conclusion

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Explanation

Proof Sequence Definition

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Explanation

Correct Formal System

Correct Answer

Explanation

Complete Formal System

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Explanation

Modus Ponens Form

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Explanation

Modus Ponens Rule

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Explanation

Equivalent Descriptions

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Explanation

Formal System Goals

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Explanation

Quran Recitation

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