# Logic Vocabulary Puzzles

Our all-new logic puzzles are a great way to hone students’ math vocabulary skills. This new version of our puzzles does NOT require any Java applets. We have crosswords puzzles with three levels of difficulty as well as a word search. All resources are interactive, engaging, and include a timer. Solutions are also provided. Choose a puzzle below to get started. Be sure to try our related activities!

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### Featured Logic Math Vocabulary Words On These Puzzles

Argument – An argument is considered valid if its conclusion logically follows from its premises, meaning that if the premises are true, then the conclusion must also be true. Validity is a fundamental concept in logic, serving as a criterion for evaluating the soundness of reasoning.

Axiom – An axiom is a statement or proposition that is accepted as true without requiring proof, serving as a fundamental assumption or starting point for deductive reasoning. Axioms are self-evident truths or basic principles that form the basis of a mathematical system or theory.

Biconditional Statement – A biconditional statement is a compound proposition that asserts that two propositions are logically equivalent, meaning they have the same truth value. It is expressed in the form “P if and only if Q” and denoted symbolically as P ↔ Q.

Conditional Statement – A conditional statement is an “if-then” statement that asserts a relationship between two propositions, where the truth of one proposition depends on the truth of the other. It is often expressed in the form “if P, then Q,” denoted symbolically as P → Q.

Conjunction – A conjunction is a compound proposition formed by joining two or more propositions with the logical connective “and.” It is true only when all component propositions are true, otherwise, it is false.

Contradiction – A contradiction is a compound proposition that is always false, regardless of the truth values of its component propositions. It occurs when the truth table for the compound proposition has only false entries, indicating that it is false under all possible truth value assignments.

Deductive Reasoning – Deductive reasoning is a method of logical reasoning in which conclusions are derived from general principles or premises through valid logical inference. It involves moving from the general to the specific and is commonly used in mathematics, logic, and formal proofs.

Disjunction – A disjunction is a compound proposition formed by joining two or more propositions with the logical connective “or.” It is true if at least one of the component propositions is true, otherwise, it is false.

Fallacy – A fallacy is a flaw in reasoning that leads to an invalid or unsound argument. Fallacies can arise from errors in logic, rhetoric, or reasoning processes and can undermine the credibility and persuasiveness of an argument.

Inductive Reasoning – Inductive reasoning is a method of logical reasoning in which conclusions are inferred from specific observations or evidence, leading to general principles or hypotheses. It involves moving from the specific to the general and is commonly used in scientific inquiry, data analysis, and everyday problem-solving.

Inference – Inference is the process of deriving new information or conclusions from existing knowledge, evidence, or premises. It involves applying logical rules and principles to draw valid conclusions from given information and is fundamental to reasoning and problem-solving.

Law of Detachment – The Law of Detachment is a fundamental principle of deductive reasoning that states if a conditional statement is true and its hypothesis is true, then its conclusion must be true. It is a basic rule used in logical arguments and mathematical proofs.

Law of Syllogism – The Law of Syllogism is a fundamental principle of deductive reasoning that states if two conditional statements are true and the conclusion of the first statement is the hypothesis of the second statement, then the conclusion of the second statement follows logically from the first. It is a key concept in logic and forms the basis for constructing logical arguments.

Logical Equivalence – Logical equivalence is a relationship between two propositions that have the same truth values under all possible truth value assignments. It means that the propositions are interchangeable in logical contexts and represent the same underlying truth.

Logic – Logic is the systematic study of reasoning and inference, examining the principles governing valid and invalid arguments. It provides a framework for evaluating the validity of arguments and making deductions based on established rules and principles.

Modus Ponens – Modus Ponens is a valid form of deductive reasoning that asserts if a conditional statement is true and its hypothesis is true, then its conclusion must be true. It is commonly expressed as “if P, then Q; P, therefore Q.”

Modus Tollens – Modus Tollens is a valid form of deductive reasoning that asserts if a conditional statement is true and its conclusion is false, then its hypothesis must be false. It is commonly expressed as “if P, then Q; not Q, therefore not P.”

Predicate Logic – Predicate logic is a formal system of logic that extends propositional logic to allow for the representation and manipulation of relationships between objects using predicates and quantifiers. It provides a more expressive and powerful framework for reasoning about statements involving variables, predicates, and quantifiers.

Predicate – In logic, a quantifier is a symbol or operator used to specify the quantity of objects that satisfy a given property or condition. The two main quantifiers are the existential quantifier (∃), which asserts that there exists at least one object with a specified property, and the universal quantifier (∀), which asserts that all objects have a specified property. Quantifiers play a crucial role in predicate logic, enabling the formalization of statements involving variables and predicates.

Proposition – In logic, a proposition is a declarative statement that is either true or false, but not both. Propositions are the basic building blocks of logical reasoning, forming the basis for logical arguments and deductions.

Proof – A proof is a logical argument or demonstration that establishes the truth of a mathematical statement or theorem beyond doubt. It involves a series of logical steps, starting from accepted axioms or premises and leading to a valid conclusion, demonstrating the validity of the statement.

Quantifier – In logic, a quantifier is a symbol or operator used to specify the quantity of objects that satisfy a given property or condition. The two main quantifiers are the existential quantifier (∃), which asserts that there exists at least one object with a specified property, and the universal quantifier (∀), which asserts that all objects have a specified property. Quantifiers play a crucial role in predicate logic, enabling the formalization of statements involving variables and predicates.

Tautology – A tautology is a compound proposition that is always true, regardless of the truth values of its component propositions. It occurs when the truth table for the compound proposition has only true entries, indicating that it is true under all possible truth value assignments.

Theorem – In mathematics, a theorem is a statement that has been proven to be true based on accepted axioms, definitions, and previously established results. Theorems play a central role in mathematics, serving as the foundation for further mathematical exploration and discovery.

Truth Value – The truth value of a proposition refers to whether the proposition is true or false in a given context or under specific conditions. Understanding truth values is essential for evaluating the validity of logical arguments and making accurate deductions.