Read the notes, then try the practice. It adapts as you go.When you're ready.
Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
8
Logic is the systematic study of valid reasoning and inference. It provides the foundational principles for distinguishing correct arguments from incorrect ones, examining the structure of statements and the relationships between premises and conclusions. Rooted in ancient Greek philosophy, particularly the work of Aristotle, logic has evolved from a branch of philosophy into a rigorous formal discipline that underpins mathematics, computer science, linguistics, and artificial intelligence.
At its core, logic investigates the forms and patterns of thought rather than the specific content of any particular argument. Formal logic uses symbolic languages and precisely defined rules to represent propositions, connectives, quantifiers, and inference steps, enabling the mechanical verification of whether a conclusion follows necessarily from its premises. Propositional logic deals with whole statements connected by operators such as 'and,' 'or,' 'not,' and 'if-then,' while predicate logic extends this framework with variables, predicates, and quantifiers to express more complex relationships about objects and their properties.
Beyond its theoretical elegance, logic has immense practical importance. It is the bedrock of mathematical proof, the design language of digital circuits and programming languages, the engine behind automated theorem provers and database query systems, and a critical tool for clear thinking in law, ethics, and everyday argumentation. The study of informal logic and critical thinking further equips individuals to identify fallacies, evaluate evidence, and construct persuasive, well-reasoned arguments in real-world discourse.
One step at a time.
The branch of logic that deals with propositions (statements that are either true or false) and the logical connectives that combine them, such as conjunction, disjunction, negation, and implication. It provides the simplest formal system for analyzing the logical structure of arguments.
Example: The argument 'If it rains, the ground is wet; it is raining; therefore the ground is wet' is a valid propositional inference known as modus ponens.
An extension of propositional logic that introduces variables, predicates, and quantifiers (universal and existential) to express properties of objects and relationships between them. It is far more expressive than propositional logic and forms the basis of most mathematical reasoning.
Example: The statement 'All humans are mortal' is formalized as 'For all x, if x is human then x is mortal,' which cannot be expressed in propositional logic alone.
An argument is valid if its conclusion necessarily follows from its premises, regardless of whether the premises are actually true. An argument is sound if it is both valid and all of its premises are in fact true. This distinction is central to evaluating arguments rigorously.
Example: The argument 'All fish can fly; Salmon is a fish; therefore Salmon can fly' is valid (the conclusion follows from the premises) but not sound (the first premise is false).
An error in reasoning that renders an argument logically invalid or seriously weakened. Formal fallacies violate the structural rules of valid inference, while informal fallacies involve errors in content, context, or relevance that undermine persuasive force.
Example: Affirming the consequent is a formal fallacy: 'If it rains, the street is wet; the street is wet; therefore it rained' is invalid because other causes could have wet the street.
A form of reasoning in which the conclusion is guaranteed to be true if the premises are true. Deductive arguments aim for certainty and are evaluated by their validity, meaning the truth of the premises necessitates the truth of the conclusion.
Example: From the premises 'All mammals are warm-blooded' and 'A whale is a mammal,' we can deductively conclude with certainty that 'A whale is warm-blooded.'
A form of reasoning in which the premises provide probabilistic support for the conclusion but do not guarantee it. Inductive arguments are evaluated by their strength, that is, how likely the conclusion is given the evidence provided.
Example: After observing that the sun has risen every morning for thousands of years, we inductively conclude that the sun will rise tomorrow, though this is not logically guaranteed.
A mathematical table used to determine the truth value of a compound proposition for every possible combination of truth values of its component propositions. Truth tables provide a mechanical method for checking validity in propositional logic.
Example: A truth table for 'P AND Q' shows that the compound statement is true only when both P and Q are individually true, yielding one true row out of four possible combinations.
A fundamental rule of inference stating that if a conditional statement ('if P then Q') is true and its antecedent (P) is also true, then its consequent (Q) must be true. It is one of the most basic and widely used valid argument forms.
Example: Given 'If the alarm sounds, then there is a fire drill' and 'The alarm sounds,' we validly conclude 'There is a fire drill.'
More terms are available in the glossary.
Choose a different way to engage with this topic — no grading, just richer thinking.
Explore your way — choose one:
See how the key ideas connect. Nodes color in as you practice.
Walk through a solved problem step-by-step. Try predicting each step before revealing it.
This is guided practice, not just a quiz. Hints and pacing adjust in real time.
Small steps add up.
What you get while practicing:
The best way to know if you understand something: explain it in your own words.
More ways to strengthen what you just learned.