- Limitations of Propositional Logic
- Predicate Logic and Predicates

Hence, some valid arguments cannot be concluded or translated into purely propositional logic.

It is not possible to mention properties that apply to categories of object, or even about relationships between those properties.

Please read the following examples carefully

- Every computer connected to the college network is functioning properly.
- Computer Science lab is functioning properly
- However, it is not possible to find out the truth about whether Business lab is functioning.

- Adam is ill.
- If Adam is ill, he should not go to school.
- So, Adam should not go to school.

- Computer X has been infected by a virus.
- Computer Y has been infected by a virus.
- However, it is not possible to say the city network has been infected by virus.

For example:

- x>9
- x=y+9
- x+y=z

A statement with variable has two parts:

- x is greater than 9
- The first part, the variable x, is the subject of the statement.
- The second partâ€”the predicate, "is greater than 9" refers to a property that the subject of the statement can have.
- We denote the statement "x is greater than 3" by P(x), where P denotes the predicate "is greater than 3" 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.

What are the truth values of P(4) and P(2)?

- P(1), which is the statement "1 > 3," is false.
- P(2), which is the statement "2 > 0," is true.

Example 2: Let A(x) denote the statement "Computer x is infltrated by a virus." Suppose CS and Business are infilitrated by a virus.

What are truth values of A(CS10), A(CS20), and A(Business)?

- A(CS10) is false, as CS1 is not on the list of infiltrated computers.
- A(CS20) and A(Business) are true, because CS20 and Business are on the list of infiltrated computers.

Example 1: Let Q(x, y) denote the statement "x = y + 9."

What are the truth values of the propositions Q(1, 2) and Q(5, 0)?

- The statement Q(1, 2) is the statement "1 = 2 + 9," which is false.
- The statement Q(5, 0) is the proposition "5 = 0 + 5," which is true.

Example 2: Let Q(x, y) denote the statement "x = y + 3.".

What are the truth values of the propositions Q(3, 2) and Q(7, 0)?

- The statement Q(3, 2) is the statement "3 = 2 + 3," which is false.
- The statement Q(7, 0) is the proposition "7 = 0 + 7," which is true.

P(x

A statement of the form P(x1, x2, . . . , xn) is the value of the propositional function P
at the n-tuple (x_{i}, x_{2}, . . . , x_{n}), and P is also called a n-ary predicate.

For more details, please contact me here.

Date of last modification: March 27, 2019