Advanced Logic

A visually striking, abstract representation of logic and reasoning concepts, featuring interconnected symbols, truth tables, and mathematical expressions in vibrant colors.

Advanced Logic Challenge

Test your skills in advanced logic with our comprehensive quiz! This specially designed quiz covers various aspects of classical logic, first-order logic, propositional calculus, and many fascinating topics within logic itself.

Whether you're a student, a teacher, or simply a logic enthusiast, this quiz will help you sharpen your analytical skills:

Multiple choice questions
Engaging and thought-provoking scenarios
Instant feedback on your answers

20 Questions5 MinutesCreated by AnalyzingMind42

Assuming classical logic, what class is the statement "¬(A→(B→A))"?

Tautology

Contradiction

Contingency

In first order logic, which of the following is equivalent to "¬∀xφ(x)"?

�x¬φ(x)

�x¬φ(x)"

�xφ(x)

¬∃xφ(x)

Under the assumption that there exists something, what is the prenex normal form of "∃x(∀y(ψ(y))→φ(x))"?

�x∀y(ψ(y)→φ(x))

�x∃y(ψ(y)→φ(x))

�x∀y(ψ(y)→φ(x))

In what order logic can we quantify over relations?

Zeroth

First

Second

Higher

In classical logic, which of the following is a not a valid deduction in sequent calculus?

A, A→B ⊢ B

¬¬p ⊢ p, q

S ⊢ S ∧ T

φ, ψ ⊢ φ

What axiom is presumed in all Hilbert Systems?

Modus Ponens

Double Negation

Modus Tollens

Contraposition

What is the relationship between the statements "p ∧ q" and "(p ∨ r) ∧ q"

Equivalent

Equisatisfiable

Duals of each other

Negations of each other

Assuming classical logic, suppose A=⊤ and B=¬A. What is the truth value of "(A↔¬B)∧(B→C)"

True

False

Contingent on C

In a binary logic, how many possible unique operators are there with arity 2?

Which of Gödel's Incompleteness Theorems apply to classical propositional logic?

Neither

The First

The Second

Both

How may the negation of some statement 'p' be defined employing only the use of truth values and implications?

P→⊥

�→p

P→p

�→⊥

When does inductive reasoning constitute proof?

Never.

If the deviation is more than 5 Sigma.

When the sample exhausts all possibilities.

If it is sound, always.

What is the domain of discourse in propositional calculus?

The alphabet.

The set of well-formed formulas.

The set of truth values.

The set of symbols.

Which of the following is not a well-formed formula?

P→q

¬(q↔r)

¬¬¬A

(a∧b)(c→d)

In a three valued logic, how many possible truth tables are there for an m by n grid?

3^(m * n)

2^(m * n)

2^(m + n)

3^(m + n)

In fuzzy logic, how many truth values are there?

None

Infinite

How many variables are there in a propositional calculus?

As many as there are operators

As many as there are axioms

As many as there are truth values

As many as there are symbols in the alphabet

As many as there are transformation rules

Which of the following sequents is invalid?

�

� ⊤

� ⊢ ⊤

Which of the following is a common metatheorem?

Hypothetical Syllogism

Double Negation

Contraposition

Modus Ponens

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