MACM 101 Chapter Notes - Chapter 2.5: Universal Quantification, Modus Ponens, Quadrilateral
15 Mar 2016
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2. 5 quantifiers, definitions, and the proofs of theorems. Example: from the universe of quadrilaterals, one person might say that: If a quadrilateral is a rectangle then it has four equal angles . Another person might say x is a rectangle. We know that the converse of an implication is not logically equivalent to the implication: we must consider what is intended. In this case each person actually refers to the biconditional where: x [p(x) q(x), a rectangle is a rectangle if and only if it has four equal angles. Statements of mathematical interest, statements that are known to be true. Sometimes used only to describe major results that have many and varied consequences: certain consequences that follow rather immediately from a therorem are called corollaries. Invalid arguments using the rule of universal specification. Let p(x): x is a square q(x): x has four sides. We are attempting to argue by the converse.
