January 7 - Logical Operators and Conditional Statements.docx

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University of North Georgia
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MATH 3500

• A proposition is a statement of fact that can be determined true or false. • A propositional variable is a letter assigned to represent a proposition. Most commonly p and q • p: it is raininq: 3+5=8 negate these with the ! or ~ symbol as in !p or ~p (read: not p) • Example: q: There are at least 12 students in the class. !q: There are greater than 12 students in the class. Negating a proposition involves using proper English grammar to state the opposite of the proposition, or what would make the original proposition false. • Truth table for the not (!) operator: p !p T F F T The not symbol is a unary operator, meaning it operates on only one number. • p: It is raining. q: 3+5=8 ^ is the AND symbol p^q means p AND q. This is true only when both p and q are true. Truth table for ^ (AND) p q P^q T T T T F F F T F F F F • v is the OR symbol p v q is true when one or the other or both is true Truth table for v (OR) p q p v q T T T T F T F T T F F F • exclusive or (XOR) Exclusively A or B, but not both
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