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

Equivalent Proposition

When two composite preposition formed out of same prime components have the same truth value for each possible combination of truth values of their prime components. We call them equivalent proposition.

{p_1} \equiv {p_2}\left( {{p_1} \Leftrightarrow {p_2}} \right)            

  • p \to q \equiv \sim p \cup q
  • q \to p \equiv \sim p \to  \sim q

Some equivalence propositions:

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