Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Contradiction

If a composite preposition is always false for all possible assignment of truth values to its prime components, then it is called contradiction. i.e,

  • p \cap \left( { \sim q} \right)
  • p \cap \left( { \sim p} \right)

Truth table

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The argument is called logically valid if the conclusions are true whenever the premises are true. Otherwise, it is called logically invalid.

The following methods are used to check the validity of statements:

  • Direct method
  • Contrapositive method
  • Method of contradiction
  • Using a counter example
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