Discrete Math Predicate Logic Predicate Statement involving variables
Discrete Math: Predicate Logic
Predicate Statement involving variables, such as “x > 5, ” “x = y + 5, ” “x + y = z, ” The previous statement are neither true nor false when the values of the variables are not specified. The statement “x is greater than 5” has two parts. The first part, the variable x, is the subject of the statement. The second part—the predicate, “is greater than 5”— refers to a property that the subject of the statement can have.
Propositional Function We can denote the statement “x is greater than 5” by P (x), where P denotes the predicate “is greater than 5” and x is the variable. The statement P(x) is also said to be the value of the propositional function P at x. Once a value has been assigned to the variable x, the statement P(x) becomes a proposition and has a truth value.
Propositional Function Example: Let P (x) denote the statement “x > 5. ” What are the truth values of P (6) and P (2)? We obtain the statement P (6) by setting x = 6 in the statement “x > 3. ” Hence, P (6), which is the statement “ 6 > 3, ” is true. However, P (2), which is the statement “ 2 > 5, ” is false.
References Discrete Mathematics and Its Applications, Mc. Graw-Hill; 7 th edition (June 26, 2006). Kenneth Rosen Discrete Mathematics An Open Introduction, 2 nd edition. Oscar Levin A Short Course in Discrete Mathematics, 01 Dec 2004, Edward Bender & S. Gill Williamson
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