Deductive Structure Statements of Logic. The Structure.

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Presentation transcript:

Deductive Structure Statements of Logic

The Structure

Conditional Statement Hypothesis If……… Conclusion Then……….. If a polygon has three sides, then it is a triangle.

Conditional Statements If you study, then you will pass the test. Conditional statement If you pass the test, then you study. Converse If you do not study, then you will not pass the test. Inverse If you do not pass the test, then you do not study. Contrapositive

Things to Remember Definitions are always reversible Theorems and postulates are sometimes reversible Theorems must be proven Postulates are accepted without proof

Conditional Notation

Chain of Reasoning If you study hard, then you make good grades. If you make good grades, then you make money. If you make money, then you buy fast cars. If you buy fast cars, then you get speeding tickets. If you study hard, then you get speeding tickets.

Theorem 3 If a conditional statement is true, then the contrapositive is also true Example: