## An introduction to logic for mathematics |

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agree in truth-value appropriate truth-table Argument biconditional Bob enjoys classical composite statements conditional statement patterns conjunction Consider the following contrapositive Definition disjunction divisible by 22 elephants are friendly enjoys classical music equivalent statement patterns exactly divisible example excellent teachers exists at least F F F F T F false statement following pattern following sentence following statement given statement Harold Hence Inclusive disjunction integers inverse—If Jane Lake Erie Law of Syllogism Let P(x Let the universal logically equivalent mathematics necessary condition negation open statement passed the examination pattern is invalid possible instance premise is true professors are excellent q has truth-value q is called q is true q p q q represent quantifier raining real numbers represent tf-statements sentence represented sentential calculus sentential statement pattern statement represented student should note sufficient condition symbolic form Today is Thursday tomorrow is Friday true statement truth-value false truth-value true universal set University of Akron Vx P(x