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Inductive reasoning

The process of reasoning that a rule or statement is true because specific cases are true.

Conjecture

A statement that is believed to be true.

Counterexample

An example that proves that a conjecture or statement is false.

Conditional Statement

A statement that can be written in the form "if p, then q," where p is the hypothesis and q is the conclusion.

Hypothesis of a Conditional Statement

The part of a conditional statement following the word if.

Conclusion of a Conditional Statement

The part of a conditional statement following the word then.

Truth value of a Conditional Statement

A statement can have a truth value of true (T) or false (F).

Negation

The negation of statement p is "not p," written as ~p.

Converse of a Conditional Statement

A statement formed by exchanging the hypothesis and conclusion of a conditional statement.

Inverse of a Conditional Statement

A statement that negates both the hypothesis an conclusion in a conditional statement.

Contrapositive of a Conditional Statement

The statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement.

Logically equivalent

A statement that has the same truth value.

Deductive Reasoning

The process of using logic to draw conclusions from given facts, definitions, and properties.

Law of Detachment

If p ➡ q is a true conditional statement and p is true, than q is true.

Law of Syllogism

If p ➡q and q➡r are ture conditional statements, then p➡r is true.