Geometry Conditional Statements (Chapter 2-2 and 2-3)

truth table

A table used as a convenient method for organizing the truth values of statements The original statement and contrapositive will ALWAYS have the same truth value. The converse and inverse will ALWAYS have the same truth value. EX: Original: If it has four legs, then it is a dog. FALSE (it could be a cat) Converse: If it is a dog, then it does have four legs. (TRUE) Inverse: If it does not have four-legs, then it is not a dog. (TRUE) Contrapositive: If it is not a dog, then it does not have four legs. FALSE (it could be a cat)

Bi-conditional Statement example

If a polygon is a triangle, it has exactly three sides. (conditional) If a polygon has exactly three sides, it is a triangle. (converse) A polygon is a triangle if and only if it has exactly three sides. (bi-conditional)

inverse

If not p, then not q

contrapositive

If not q, then not p

converse

If q, then p

Example of Contrapositive

Original Statement: If today is Wednesday, then tomorrow is Thursday. Contrapositive: If tomorrow is not Thursday, then today is not Wednesday.

Example of Converse

Original Statement: If today is Wednesday, then tomorrow is Thursday. Converse Statement: If tomorrow is Thursday, then today is Wednesday.

Example of Inverse

Original statement: If today is Wednesday, then tomorrow is Thursday. Inverse Statement: If today is not Wednesday, then tomorrow is not Thursday.

bi-conditional statement

a statement that can be written in the form "p if and only if q" where p is a true conditional statement and q is the converse of p and it is also true

Counterexample

an example that proves that a conjecture or statement is false