Category: 04. Logic & Propositional

The problem of finding whether a given statement is tautology or contradiction or satisfiable in a finite number of steps is called the Decision Problem. For Decision Problem, construction of truth table may not be practical always. We consider an alternate procedure known as the reduction to normal forms. There are two such forms: Disjunctive…

Predicate Logic deals with predicates, which are propositions, consist of variables. Predicate Logic – Definition A predicate is an expression of one or more variables determined on some specific domain. A predicate with variables can be made a proposition by either authorizing a value to the variable or by quantifying the variable.The following are some…

Tautologies A proposition P is a tautology if it is true under all circumstances. It means it contains the only T in the final column of its truth table. Example: Prove that the statement (p⟶q) ↔(∼q⟶∼p) is a tautology. Solution: Make the truth table of the above statement: p q p→q ~q ~p ~q⟶∼p (p→q)⟷( ~q⟶~p) T…

Conditional Statement Let p and q are two statements then “if p then q” is a compound statement, denoted by p→ q and referred as a conditional statement, or implication. The implication p→ q is false only when p is true, and q is false; otherwise, it is always true. In this implication, p is…

Negation: It means the opposite of the original statement. If p is a statement, then the negation of p is denoted by ~p and read as ‘it is not the case that p.’ So, if p is true then ~ p is false and vice versa. Example: If statement p is Paris is in France, then ~…

A Proposition or a statement or logical sentence is a declarative sentence which is either true or false. Example1: The following statements are all propositions: Example2: The following statements are not propositions: Propositional Variables The lower case letters starting from P onwards are used to represent propositions Example: p: India is in Asia           …