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

Negation of Compound Statement

  • Negation of conjunction:

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

  • Negation of disjunction:

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

  • Negation of negation:

 \sim \left( { \sim p} \right) \equiv p

  • Negation of conditional:

 \sim \left( {p \to q} \right) \equiv p \cap  \sim q

  • Negation of conjunction:

 \sim \left( {p \leftrightarrow q} \right) \equiv \left( {p \cap  \sim q} \right) \cup \left( {q \cap  \sim p} \right).

  • Negation of quantified statement:

While finding the negations of quantified statements, the word ‘all’ is replaced by ‘some’ and ‘for every’ or ‘for all’ is replaced by ‘there exist’ and vice-versa.

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