The process of reasoning that a rule or statement is true because specific cases are true.
A statement that is believed to be true.
An example that proves that a conjecture or statement is false.
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).
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.
A statement that has the same truth value.
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.