About this Study Set
This study set covers Logic through
18 practice questions.
This quiz tests knowledge of key figures, dates, and numerical concepts in the history and development of formal logic. Every question includes the correct answer so you can learn as you go — pick any format above to get started.
Questions & Answers
Browse all 18 questions from the
Foundations of Formal Logic study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
In what year did Gottlob Frege publish 'Begriffsschrift', a seminal work introducing quantifiers and propositional calculus?
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A
1879
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B
1884
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C
1893
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D
1902
2
Which philosopher, in 1910, co-authored 'Principia Mathematica' which aimed to derive all mathematical truths from logical axioms?
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A
Gottlob Frege
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B
Bertrand Russell
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C
David Hilbert
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D
Kurt Gödel
3
The standard definition of a 'consistent' set of formulas in first-order logic is one from which no contradiction (represented as 'P and not P') can be derived. How many distinct truth values are there in classical propositional logic?
4
Alfred Tarski's work on the concept of truth was significantly developed in a paper published in which year?
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A
1933
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B
1936
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C
1944
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D
1950
5
Kurt Gödel's incompleteness theorems were first presented in a paper published in 1931. How many incompleteness theorems are generally attributed to Gödel?
6
The notation '∀' for universal quantification was introduced by Gottlob Frege. Approximately how many distinct symbols were used in the original formulation of Frege's 'Begriffsschrift'?
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A
Around 20
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B
Around 50
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C
Around 100
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D
Around 200
7
The Łukasiewicz logic, named after Jan Łukasiewicz, introduced many-valued logic. In his early work on three-valued logic in 1920, what was the third truth value he introduced?
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A
Indeterminate
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B
Possible
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C
Contingent
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D
Unknown
8
George Boole published 'An Investigation of the Laws of Thought' in what year, laying the groundwork for Boolean algebra?
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A
1847
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B
1854
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C
1864
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D
1874
9
How many variables are typically required to represent all possible truth-functional relationships between two propositions in propositional logic?
10
The logical connective 'material implication' (if... then...) is often represented by the symbol '→'. How many rows are in a truth table for two propositional variables?
11
Which logician is credited with formalizing the concept of a 'recursive function' in 1934, a key development in computability theory and logic?
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A
Kurt Gödel
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B
Alonzo Church
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C
Alan Turing
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D
Stephen Kleene
12
The principle of explosion states that from a contradiction, anything can be proven. In classical logic, 'P ∧ ¬P' implies 'Q' for any proposition 'Q'. How many distinct ways can the biconditional 'P ↔ Q' be true?
13
David Hilbert's program, aiming to establish the consistency of mathematics, was influential in the early 20th century. In which decade did he first formally outline his program?
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A
1900s
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B
1910s
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C
1920s
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D
1930s
14
The satisfiability problem (SAT) is a fundamental problem in computational logic. It asks whether a given propositional logic formula can be made true. For a formula with 'n' variables, what is the maximum number of possible truth assignments?
15
In modal logic, '□' represents necessity. How many distinct logical axioms are fundamental to the standard modal system K?
16
The concept of a 'model' in logic refers to an interpretation under which a formula is true. How many distinct models can a simple propositional formula with one variable have at most?
17
The proof of the completeness of first-order logic was first provided by Kurt Gödel in which year?
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A
1929
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B
1930
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C
1931
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D
1932
18
The term 'tautology' refers to a formula that is always true, regardless of the truth values of its components. For a propositional logic formula with 3 variables, how many distinct truth values can be evaluated across all possible assignments?
