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

Algebra of Statement: Some Standard Equivalence Relation

Some standard equivalence relation

Idempotent law:

  • p \cup p \equiv p
  • p \cap p \equiv p

Identity law:

  • p \cup F \equiv p
  • p \cap F \equiv F
  • p \cup T \equiv T
  • p \cap T \equiv p

Complement law:

  • p \cup  \sim p \equiv T
  • p \cap  \sim p \equiv F

Involution law:

  •  \sim T \equiv F
  •  \sim F \equiv T
  •  \sim \left( { \sim p} \right) \equiv p

Commutative law:

  • p \cup q \equiv q \cup p
  • p \cap q \equiv q \cap p

Associative laws:

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

Distributive law:

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

Absorption law:

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

Conditional law:

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

De Morgan’s law

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