About this Study Set
This study set covers Logic through
25 practice questions.
A comprehensive quiz on the logical principles underpinning formal systems, mathematics, and computing. Every question includes the correct answer so you can learn as you go — pick any format above to get started.
Questions & Answers
Browse all 25 questions from the
Scientific Foundations of Logic study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
Which law of classical logic states that for any proposition, either that proposition is true or its negation is true?
-
A
Law of Identity
-
B
Law of Non-Contradiction
-
C
Law of Excluded Middle
-
D
Law of Sufficient Reason
2
In propositional logic, what is the result of a 'conjunction' (AND) operation if both inputs are false?
-
A
True
-
B
False
-
C
Null
-
D
Undefined
3
Who is credited with developing the first formal system of deductive reasoning known as the syllogism?
-
A
Aristotle
-
B
Plato
-
C
Euclid
-
D
Pythagoras
4
What term describes a logical argument where the conclusion necessarily follows from the premises?
-
A
Inductive
-
B
Abductive
-
C
Valid
-
D
Heuristic
5
In Boolean algebra, which logical operator is equivalent to the 'NOR' gate if followed by a 'NOT' gate?
6
Which 19th-century mathematician introduced the binary system as the foundation for modern logical algebra?
-
A
Alan Turing
-
B
George Boole
-
C
Charles Babbage
-
D
Ada Lovelace
7
What is the name of the logical fallacy that assumes a conclusion is true simply because it has not been proven false?
-
A
Ad Hominem
-
B
Argumentum ad Ignorantiam
-
C
Post Hoc Ergo Propter Hoc
-
D
Straw Man
8
In predicate logic, what symbol represents the 'universal quantifier'?
9
Which theorem by Kurt Gödel proves that any consistent formal system capable of arithmetic contains unprovable statements?
-
A
Incompleteness Theorem
-
B
Completeness Theorem
-
C
Compactness Theorem
-
D
Fixed-point Theorem
10
What type of logic allows for truth values between 0 and 1, representing degrees of truth?
-
A
Binary Logic
-
B
Fuzzy Logic
-
C
Propositional Logic
-
D
Predicate Logic
11
Which logical connective produces a true value only if both input values are identical?
-
A
XNOR
-
B
XOR
-
C
NAND
-
D
NOR
12
In formal logic, what is the inverse of the implication 'If P, then Q'?
-
A
If Q, then P
-
B
If not P, then not Q
-
C
If not Q, then not P
-
D
P if and only if Q
13
Which logical principle asserts that 'A is A'?
-
A
Law of Identity
-
B
Law of Non-Contradiction
-
C
Law of Excluded Middle
-
D
Double Negation
14
What is the logical equivalent of 'P OR Q' in terms of implication?
-
A
If P, then Q
-
B
If not P, then Q
-
C
If Q, then P
-
D
If P, then not Q
15
Which logical operator returns true only if the inputs are different?
16
In a truth table for 'If P, then Q', what is the result when P is false and Q is true?
-
A
True
-
B
False
-
C
Indeterminate
-
D
Contradictory
17
Which mathematician and logician is known for his work on the 'Principia Mathematica'?
-
A
Bertrand Russell
-
B
Gottlob Frege
-
C
David Hilbert
-
D
Alfred Tarski
18
What does the logical term 'tautology' refer to?
-
A
A statement that is always false
-
B
A statement that is always true
-
C
A circular argument
-
D
A premise based on opinion
19
In classical logic, what is the 'Law of Non-Contradiction' formally defined as?
-
A
Not (P and Not P)
-
B
P or Not P
-
C
If P, then P
-
D
P equals P
20
What is the primary difference between deductive and inductive reasoning?
-
A
Deduction moves from specific to general
-
B
Induction moves from general to specific
-
C
Deduction guarantees truth if premises are true
-
D
Induction guarantees truth if premises are true
21
Which branch of logic deals with the properties of sets and their memberships?
-
A
Propositional Logic
-
B
Set Theory
-
C
Modal Logic
-
D
Temporal Logic
22
In modal logic, what does the 'diamond' symbol (◇) typically represent?
-
A
Necessity
-
B
Possibility
-
C
Obligation
-
D
Permission
23
What is a 'contingent' proposition in logic?
-
A
A statement that is always true
-
B
A statement that is always false
-
C
A statement that can be true or false depending on the situation
-
D
A statement that is self-contradictory
24
Which logician developed the concept of the 'Turing Machine' to model algorithmic computation?
-
A
Alan Turing
-
B
John von Neumann
-
C
Claude Shannon
-
D
Kurt Gödel
25
What is the logical negation of the statement 'All cats are mammals'?
-
A
No cats are mammals
-
B
Some cats are not mammals
-
C
All mammals are cats
-
D
Some mammals are not cats
