Propositional Logic - Review

Reviews key techniques and main ideas for propositional logic.

download Export

search_insights Statistics

stylus_note White Board

Quran

calculate Calculator

dictionary Dictionary

fullscreen Full Screen

more_vert More

QUESTION OF

volume_mute Read quiz aloud

Views #: 99

Questions #: 18

Time: 20 minutes

Pass Score: 80.0%

Style

Step

List

Mode

Exam

Practice

Technique: Apply Derivation Rules

1 pts

volume_mute

Which technique involves using the rules of the formal system to move from hypotheses to a conclusion?

Replace all wffs with statement letters.

Apply derivation rules for propositional logic.

Ignore the hypotheses.

Build a truth table for every statement.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Technique: Verbal Argument Validity

1 pts

volume_mute

Which technique involves translating an English argument and then proving it valid?

Change the conclusion to match the hypotheses.

Use only informal reasoning.

Avoid symbolic representation.

Use propositional logic to prove the validity of a verbal argument.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Main Idea: Valid Argument Form

1 pts

volume_mute

A valid argument can be represented by a wff of what form?

\(P_1∧P_2∧...∧P_n↔Q\), which is a contingency

\(P_1∨P_2∨...∨P_n→Q\), which is a contradiction

\(P_1→P_2→...→P_n\), which is a hypothesis

\(P_1∧P_2∧...∧P_n→Q\), which is a tautology

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Main Idea: Proof Sequence

1 pts

volume_mute

In a formal logic system, what is a proof sequence?

A set of invalid arguments.

A list of all possible truth assignments.

A sequence of wffs that are either hypotheses or derived from earlier wffs by derivation rules.

A sequence of conclusions only.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

System Properties

1 pts

volume_mute

What properties does the propositional logic system have?

It is incomplete but correct.

It is complete but incorrect.

It is neither complete nor correct.

It is complete and correct.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Meaning of Correctness

1 pts

volume_mute

What does correctness of the propositional logic system mean?

Every argument is provable.

No argument is provable.

Every valid argument is provable.

Only valid arguments are provable.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Meaning of Completeness

1 pts

volume_mute

What does completeness of the propositional logic system mean?

Only valid arguments are provable.

Every hypothesis is false.

Every proof sequence is invalid.

Every valid argument is provable.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Equivalence Rules and Truth

1 pts

volume_mute

What does it mean that equivalence rules are truth-preserving?

A false wff becomes true after substitution.

Truth values alternate after each substitution.

A true wff remains true if an equivalent substitution is made within it.

No substitutions are allowed.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Inference Rules Direction

1 pts

volume_mute

Which statement about inference rules is correct?

They do not work in both directions.

They can always be reversed.

They work in both directions.

They are identical to equivalence rules.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Deduction Method Use

1 pts

volume_mute

When is the deduction method used?

When there are no hypotheses.

When the conclusion is a contradiction.

When the conclusion is a conjunction.

When the conclusion is an implication.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Hypothetical Syllogism

1 pts

volume_mute

What does hypothetical syllogism allow?

From \(P\) and \(P→Q\), derive \(Q\).

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

From \(P\) and \(Q\), derive \(P∧Q\).

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

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Modus Ponens

1 pts

volume_mute

What does modus ponens allow?

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

From \(P∧Q\), derive \(P\).

From \(P\) and \(Q\), derive \(P∧Q\).

From \(P\) and \(P→Q\), derive \(Q\).

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Modus Tollens

1 pts

volume_mute

What does modus tollens allow?

From \(P∧Q\), derive \(Q\).

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

From \(P\) and \(Q\), derive \(P∧Q\).

From \(P\) and \(P→Q\), derive \(Q\).

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Verbal Argument Keywords

1 pts

volume_mute

Which keywords help translate a verbal argument into symbolic form?

Only negations

Only numbers

If... then, either... or, and therefore

Only nouns and verbs

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Purpose of Formal Logic

1 pts

volume_mute

Why develop formal logic for propositional arguments even though truth tables provide a mechanical test?

Because propositional logic has no derivation rules.

It serves as a dry run for predicate logic, where no mechanical tautology test exists.

Because verbal arguments cannot be symbolized.

Because truth tables are always incorrect.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Validity and Actual Truth

1 pts

volume_mute

Does the validity of an argument depend on the actual truth of its components?

No, it depends only on logical form.

No, it depends on the number of hypotheses.

Yes, it depends on the actual truth of every component.

Yes, it depends on whether the conclusion is true in real life.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Valid Argument Representation

1 pts

volume_mute

What wff represents a valid argument?

\(P_1∨P_2∨...∨P_n→Q\), where the wff is a contradiction

\(P_1∧P_2∧...∧P_n→Q\), where the wff is a tautology

\(P_1→P_2→...→P_n\), where the wff is a hypothesis

\(P_1∧P_2∧...∧P_n↔Q\), where the wff is a contingency

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Hypotheses and Conclusion

1 pts

volume_mute

In \(P_1∧P_2∧...∧P_n→Q\), what are \(P_1,...,P_n\) and \(Q\)?

\(P_1,...,P_n\) are conclusions; \(Q\) is a hypothesis.

\(P_1,...,P_n\) are hypotheses; \(Q\) is the conclusion.

\(P_1,...,P_n\) are rules; \(Q\) is a proof sequence.

\(P_1,...,P_n\) are tautologies; \(Q\) is a contradiction.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Year 11 Year 12

Technique: Apply Derivation Rules

Correct Answer

Explanation

Technique: Verbal Argument Validity

Correct Answer

Explanation

Main Idea: Valid Argument Form

Correct Answer

Explanation

Main Idea: Proof Sequence

Correct Answer

Explanation

System Properties

Correct Answer

Explanation

Meaning of Correctness

Correct Answer

Explanation

Meaning of Completeness

Correct Answer

Explanation

Equivalence Rules and Truth

Correct Answer

Explanation

Inference Rules Direction

Correct Answer

Explanation

Deduction Method Use

Correct Answer

Explanation

Hypothetical Syllogism

Correct Answer

Explanation

Modus Ponens

Correct Answer

Explanation

Modus Tollens

Correct Answer

Explanation

Verbal Argument Keywords

Correct Answer

Explanation

Purpose of Formal Logic

Correct Answer

Explanation

Validity and Actual Truth

Correct Answer

Explanation

Valid Argument Representation

Correct Answer

Explanation

Hypotheses and Conclusion

Correct Answer

Explanation

Quran Recitation

Query Dictionary

Select a result: