EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...
EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...
EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...
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Other logical operators and truth tables<br />
• You can take the negation of any proposition, whether or not it is true or<br />
false. The result will be a new proposition with the opposite truth value.<br />
• We express this using a simple display called a truth table.<br />
• The truth table for negation is<br />
p ¬p<br />
T F<br />
F T<br />
• We now introduce two new operators called conjunction and disjunction.<br />
(These are also called “and” and “or”.)<br />
• Examples (relative to today) p is “it is raining today” and q is “today is<br />
Friday”. The proposition “p and q”, notated p ∧ q, is “it is raining today<br />
and today is Friday”. The proposition “p or q, notated p∨q, is “it is raining<br />
today or today is Friday.”<br />
• The truth tables for conjunction and disjunction:<br />
p q p ∧ q<br />
T T T<br />
T F F<br />
F T F<br />
F F F<br />
p q p ∨ q<br />
T T T<br />
T F T<br />
F T T<br />
F F F<br />
6
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