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Saturday, 11 August 2012

GATE 2013 Preparation (11-08-2012)

 
MATHEMATICAL LOGIC
PROPOSITIONAL LOGIC
Introduction:
A proposition is a declarative statement that is either true or false but not both.
For example, "My name is Sam" is a declarative statement but "what is your name?" is not a declarative statement.
Tautology:
A compound proposition that is always true irrespective of the truth values of the constituent propositions is called a tautology.
Contradiction:
A compound proposition that is always false irrespective of the truth values of the constituent propositions is called a contradiction.
Proposition that is neither tautology nor a contradiction is called a contingency.
Atomic or primary statements:
Statements without connectives like 'but', 'or', 'and' are called atomic or primary statements.
Conjunction:
 Let P and Q be two statements. Then the statement "P and Q" denoted by P^Q is called the conjunction of P and Q.
Statement P^Q is true if both P and Q are true
Disjunction:
Let P and Q be two statements. Then the statement "P and Q" denoted by P^Q is called the conjunction of P and Q.
Statement PvQ is true if any one of P or Q is true




Truth Table for Conjunction, Disjunction and Negation

Conditional:
Let P and Q be two statements. Then the statement "if P then Q" denoted by P ->Q is called the Conditional Statement of P and Q.
Statement P->Q is false if P is true and Q is false else true
Note: P->Q is not same as Q->P

Biconditional:
Let P and Q be two statements. Then the statement " P if and only if Q" denoted by P< ->Q is called the Biconditional Statement of P and Q.
Statement P<->Q is true if both P and Q are same else false.
Note: P<->Q is same as Q<->P

Truth Table for Conditional and Biconditional



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