Propositional logic and Predicate logic dstl notes

Propositional logic and Predicate logic

Proposition :- Proposition is a statement which is either true or false but not both.

Compound Proposition :- A compound proposition is formed by composition of two or more propositions called components or Sub-propositions.

Conjuction:- If p and q are two propositions Then conjuction of p and q is a proposition which is true when both p and q are true otherwise false                                            Truth Table:                                                                                       

                                                                                                                                                                                                                                                                                                                                                                                                        

Disjunction :-  If p and q be two proposition , then disjunction of p and q is a proposition which is true when either one of p or q or both are true and is false when both  p and q are false.

                                                                                                                 Truth Table:- 

                                                                                                

 Negation:-If p is proposition then negation of P is a proposition which is true when p is false and false when p is true.                                                                                                    Truth table :-                                                                                                                               

 Tautologies :-A Compound proposition that is always true for all possible true values of its propositional variables and it contains T in last column of its truth table then,it is known as tautology.

Propositions like, i. The doctor is either male or female.  ii. Either it is raining or not.   – are always true and tautologies.

Contradiction :- A compound proposition that is always false for all possible truth truth values ofits propositional variables and it contains F in last coloumn of its truth table then, it is known as contradiction.

i. x is even and x is odd number .

ii. Adarsh is good boy and Adarsh is bad boy.

are always false and contradiction.

Contigency :- A proposition which is neither tautology nor contradiction is called contingency. Here the last column of truth table contains both T and F.

Satisfiability :- A compound statement formula A (P1,P2,…Pn) is said to be satisfiable , if it has a truth value T for at least one combination of truth value of P1,P2,…Pn.

Algebra of Propositions :-
Theory of Inference in Propositional Logic :-
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