What is Predicate?
“Computer x is functioning properly”
This statement has two parts. The first part, the variable x, is the subject of the statement. The second part—the predicate, “is functioning properly”—refers to a property that the subject can have.
- Universal Quantifier: The universal quantification of P(x) is the statement
“P(x) for all values of x in the domain.”
The notation ∀x P(x) denotes the universal quantification of P(x).
- Essential Quantifier: The existential quantification of P(x) is the proposition
“There exists an element x in the domain such that P(x).”
We use the notation ∃x P(x) for the existential quantification of P(x).
What is Predicates
- P(x): Propositional statement with one variable.
- Q(x, y): Propositional statement with two variables.
What is Logical Equivalences
Translating from English into Logical Expressions
(1) “You can access the Internet from campus only if you are a computer science major or you are not a freshman.”
a = “You can access the Internet from campus”
c = “You are a computer science major”
f = “You are a freshman”
a → (c ∨¬f )
(2) “Every student in this class has studied calculus”
C(x): “x has studied calculus.”
If the domain is a student in this class.
If the domain is all people in this world then.
S(x): “person x is in this class”
∀x (S(x) → C(x))
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