MATH-UA 120 Lecture Notes - Lecture 7: Contraposition, Modus Ponens, Logical Biconditional
Document Summary
Coplanar points are points all in one plane. Collinear points are points all in one line. The intersection of two figures is the set of points that are in both figures. Adjacent angles are two angles in a plane that have a common vertex and a common side by no common interior points: using deductive reasoning. P is the hypothesis while q is the conclusion. A conditional is false if an example can be found for which the hypothesis is true and the conclusion is false. A statement that contains the words if and only if is called a biconditional. A biconditional is true when the truth values of the simple statements match. A disjunction is false when both simple statements are false. Law of detachment (modus ponens): if a conditional is true and its hypothesis is true, then the conclusion is true. Law of conjunctive simplification: if a conjunction is true, then both of the simple statements are true.
