CIS 1166 Lecture Notes - Lecture 4: Existential Quantification, Universal Quantification, Empty Set
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A compound proposition is satisfiable if there is an assignment of truth values to its variables that make it true. If a compound proposition is not satisfiable, then it is called unsatisfiable. Note that an unsatisfiable proposition is a contradiction. A predicate is a sentence that contains one or more variables. Each variable can take values from a specified domain (data type). Upon substituting a value from the associated data type for each variable gives a proposition. The predicate is that x is greater than 3. P(4,3) : 4 - 3 = 1 -> true. Else end (for all, for every) (there exists, for some) P(x) : x > 3 x an integer. There exists an integer x such that x > 3. Not uq x p(x) eq x not p(x) Not eq x p(x) uq x not p(x) The examples he used were regarding students getting a"s. P(x) : the word x contains the letter a.