# Difference between Propositional Logic and Predicate Logic

• Difficulty Level : Basic
• Last Updated : 10 Jan, 2022

Logical reasoning forms the basis for a huge domain of computer science and mathematics. They help in establishing mathematical arguments, valid or invalid.

1. Propositional Logic :
A proposition is basically a declarative sentence that has a truth value. Truth value can either be true or false, but it needs to be assigned any of the two values and not be ambiguous. The purpose of using propositional logic is to analyze a statement, individually or compositely.

For example :
The following statements :

1. If x is real, then x2 > 0
3. (a+b)2 = 100
4. This statement is false.
5. This statement is true.

Are not propositions because they do not have a truth value. They are ambiguous.

But the following statements :

1. (a+b)2 = a2 + 2ab + b2
2. If x is real, then x2 >= 0
3. If x is real, then x2 < 0
4. The sun rises in the east.
5. The sun rises in the west.

Are all propositions because they have a specific truth value, true or false.

The branch of logic that deals with proposition is propositional logic.

2. Predicate Logic :
Predicates are properties, additional information to better express the subject of the sentence. A quantified predicate is a proposition , that is, when you assign values to a predicate with variables it can be made a proposition.

For example :

In P(x) : x>5, x is the subject or the variable and ‘>5’ is the predicate.

P(7) : 7>5 is a proposition where we are assigning values to the variable x, and it has a truth value, i.e. True.

The set of values that the variables of the predicate can assume is called the Universe or Domain of Discourse or Domain of Predicate.

Difference between Proposit

l Logic and Predicate Logic :

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