DISCRETE MATH: LECTURE 3 DR. DANIEL FREEMAN 1. Chapter 2.2 Conditional Statements If p and q are statement variables, the conditional of q by p is "If p then q" or "p implies q" and is denoted p !q. It is false when p is true and q is false; otherwise it is true. We call p the hypothesis (or antecedent) of the conditional and q the
Discrete Mathematics Online Lecture Notes via Web. Conditional Statements The compound proposition implication. p q. is a conditional statement, and can be read as ``if p then q'' or ``p implies q''. Its precise definition is given by the following truth table
Definition: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion. A truth table for p q is shown below.
In mathematical reasoning, to infer a conclusion we frequently make use of if-then statements. A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion.
Converse, Inverse, Contrapositive Given an if-then statement "if p , then q ," we can create three related statements: A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.
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DISCRETE MATH: LECTURE 4 DR. DANIEL FREEMAN 1. Chapter 3.1 Predicates and Quantified Statements I A predicate is a sentence that contains a nite number of variables and becomes a statement when speci c values are substituted for the variables. The domain of a predicate variable is the set of all values that may be substituted in place of the ...
A disjunction is true if either statement is true or if both statements are true! In other words, the statement 'The clock is slow or the time is correct' is a false statement only if both parts are false! Likewise, the statement 'Mr. G teaches Math or Mr. G teaches Science' is true if Mr. G is teaches science classes as well as math classes!