Discrete Mathematics
Predicates
,Predicates
• Statements involving variables, such as x> 5 and x+y=z, are often
found in mathematical assertions and in computer programs.
• These statements are neither true nor false, when the values of
the variables are not specified.
Example: x> 5
The statement “x is greater than 5” has two parts
First part: The variable x, is the subject of the statement
Second part: The predicate, is “greater than 5” refers to a property
that the subject
We can denote the statement “x is greater than 5” by P(x), here P
denote the predicate and x is the variable.
9/2/2024 Indian Institute of Information Technology, Kottayam 2
, Note:
1. The statement P(x) is also said to be the value of the
propositional function P at x.
2. Once a value has been assigned to the variable x, the statement
P(x) becomes a proposition and has a truth value.
Example:
Let P(x) denote the statement “x> 5”. What are the truth value of
P(6) and P(3).
Solution: Given statement “x> 5”
Hence P(6) ⇒ “6> 5” is true
P(3) ⇒ “3> 5” is false
9/2/2024 Indian Institute of Information Technology, Kottayam 3
Predicates
,Predicates
• Statements involving variables, such as x> 5 and x+y=z, are often
found in mathematical assertions and in computer programs.
• These statements are neither true nor false, when the values of
the variables are not specified.
Example: x> 5
The statement “x is greater than 5” has two parts
First part: The variable x, is the subject of the statement
Second part: The predicate, is “greater than 5” refers to a property
that the subject
We can denote the statement “x is greater than 5” by P(x), here P
denote the predicate and x is the variable.
9/2/2024 Indian Institute of Information Technology, Kottayam 2
, Note:
1. The statement P(x) is also said to be the value of the
propositional function P at x.
2. Once a value has been assigned to the variable x, the statement
P(x) becomes a proposition and has a truth value.
Example:
Let P(x) denote the statement “x> 5”. What are the truth value of
P(6) and P(3).
Solution: Given statement “x> 5”
Hence P(6) ⇒ “6> 5” is true
P(3) ⇒ “3> 5” is false
9/2/2024 Indian Institute of Information Technology, Kottayam 3
