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12 Cards in this Set
- Front
- Back
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Describe "Discrete Mathematics"
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- based on the variation of a variable through integers
- integers are based on a discrete subset of <i>real numbers </i> - in the broader sense, Discrete Math studies countable structures |
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Real Numbers
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-76, -3, 0, 1, 57....etc
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Propositions
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- The basic building block of logic
- A declaritive statement that is either TRUE or FALSE but NOT both or neither. - Not a question! |
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Truth Value
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- can be either T (true) or F (false)
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Atomic Proposition
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- A simple statement that is not the combination of 'simpler statements'
"The moon is blue" as opposed to ... "The moon is blue and you are too!" |
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Logical Operators
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- We can construct new propositions from old ones using logical operators.
- With the exception of negation, all operators are logical connective operators. |
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Negation
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- Pronounced "Not p"
- Written " p" When "p" is TRUE, " p" is FALSE |
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Conjunction
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- Pronounced "p OR q"
- Written "p q" "p q" is TRUE when BOTH are TRUE, and is otherwise FALSE |
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Disjunction
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- Pronounced "p AND q"
- Written "p q" "p q" is TRUE if at least one of p,q is TRUE and FALSE only if both p,q are FALSE |
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Exclusive Or
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- Pronounced "p X Or q"
- Written "p q" "p q" is TRUE if exactly one of p,q is TRUE and FALSE otherwise |
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Truth Tables
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- Allow us to exhibit all the possible truth values of compound propositions (that are combinations of simpler propositions)
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Compound Proposition
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- A proposition that has 2 or more propositions joined by logical connective opperators
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