Propositions and
Predicates
Mathematical logic is the foundation on which the proofs and arguments rest.
Propositions are statements used in mathematical logic, which are either true
or false but not both and we can definitely say whether a proposition is true
or false.
In this chapter we introduce propositions and logical connectives. Normal
forms for well-formed formulas are given. Predicates are introduced. Finally,
\ve discuss the rules of inference for propositional calculus and predicate calculus.
1.1 PROPOSITIONS (OR STATEMENTS)
A proposition (or a statement) is classified as a declarative sentence to which
only one of the truth values. i.e. true or false. can be assigned. When a
proposition is true, we say that its truth value is T. When it is false, we say
that its truth value is F.
Consider. for example. the following sentences in English:
1. New Delhi is the capital of India.
'1
The square of 4 is 16.
3. The square of 5 is 27.
4. Every college will have a computer by 2010 A.D.
S. Mathematical logic is a difficult subject.
6. Chennai is a beautiful city.
7. Bring me coffee.
8. No. thank you.
9. This statement is false.
The sentences 1-3 are propositions. The sentences 1 and 2 have the truth value
T. The sentence 3 has the truth value F. Although we cannot know the truth
value of 4 at present. we definitely know that it is true or false, but not both.
1
http://engineeringbooks.net
Predicates
Mathematical logic is the foundation on which the proofs and arguments rest.
Propositions are statements used in mathematical logic, which are either true
or false but not both and we can definitely say whether a proposition is true
or false.
In this chapter we introduce propositions and logical connectives. Normal
forms for well-formed formulas are given. Predicates are introduced. Finally,
\ve discuss the rules of inference for propositional calculus and predicate calculus.
1.1 PROPOSITIONS (OR STATEMENTS)
A proposition (or a statement) is classified as a declarative sentence to which
only one of the truth values. i.e. true or false. can be assigned. When a
proposition is true, we say that its truth value is T. When it is false, we say
that its truth value is F.
Consider. for example. the following sentences in English:
1. New Delhi is the capital of India.
'1
The square of 4 is 16.
3. The square of 5 is 27.
4. Every college will have a computer by 2010 A.D.
S. Mathematical logic is a difficult subject.
6. Chennai is a beautiful city.
7. Bring me coffee.
8. No. thank you.
9. This statement is false.
The sentences 1-3 are propositions. The sentences 1 and 2 have the truth value
T. The sentence 3 has the truth value F. Although we cannot know the truth
value of 4 at present. we definitely know that it is true or false, but not both.
1
http://engineeringbooks.net