Discrete Maths : Introduction to Propositional & Predicate Logic (Part-2)

By Anand Pandey|Updated : August 25th, 2021

PREDICATE LOGIC

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.

PREDICATE LOGIC

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.

 Quantifiers

  • 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.

 Note:

 byjusexamprep

What is Logical Equivalences

 

 byjusexamprep

byjusexamprep

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.

          x C(x)

      If the domain is all people in this world then.

     S(x): “person x is in this class”

       x (S(x) C(x))

Thanks,

Sahi Prep Hai Toh Life Set Hai!

Comments

write a comment

Follow us for latest updates