Converse, Inverse, Contrapositive

Conditional Statement

a statement written in "if then" form

Hypothesis

the "if" part of a conditional statement

Conclusion

the "then" part of a conditional statement

Counter Example

an example given where the hypothesis is true and the conclusion is false. example: "if p, then q"

Converse

a statement made my switching the hypothesis and conclusion of a conditional statement. example: "if q, then p"

Inverse

a statement made by negating the hypothesis and conclusion of a conditional statement example: "if not p, then not q"

Contrapositive

a statement made by negating and switching the hypothesis and conclusion of a conditional statement example: "if not q, then not p"

Biconditional Statement

when a conditional statement and its converse are true, they can be written as one statement using "if and only if" example: "p if and only if q"

inductive reasoning

Is the process of reasoning that a rule or statement is true because specific cases are true

deductive reasoning

reasoning in which a conclusion is reached by stating a general principle and then applying that principle to a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.)

Law of Detachment

If p --> q is a true statement and p is true, then q is true

Law of Syllogism

If p-->q and q-->r are true statements, then p-->r is a true statement.