Advanced Logic
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
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)"?
ˆƒx¬φ(x)
ˆ€x¬φ(x)"
ˆƒxφ(x)
¬∃xφ(x)
Under the assumption that there exists something, what is the prenex normal form of "∃x(∀y(ψ(y))→φ(x))"?
ˆƒx∀y(ψ(y)→φ(x))
ˆ€x∃y(ψ(y)→φ(x))
ˆƒx∃y(ψ(y)→φ(x))
ˆ€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
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→⊥
Š¥â†’p
P→p
Š¥â†’⊥
Which of the following is not a functionally complete set of connectors?
{¬, ∧}
{¬, ∨}
{NAND}
{¬, →}
{¬,↔}
{NOR}
{⊥, →}
{⊥, ∧, ↔}
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
1
2
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?
Š¢
Š¢ ⊤
Š¥ ⊢ ⊤
Which of the following is a common metatheorem?
Hypothetical Syllogism
Double Negation
Contraposition
Modus Ponens
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