List of Equivalence Formulas

In this class, We discuss List of Equivalence Formulas

The reader should have prior knowledge of the equivalence of two propositions. Click Here.

Below is the list of equivalent formulas.

1) Idempotent Law

P ∨ P <=> P

P ∧ P <=> P

2) Associative Law

(P ∨ Q) ∨ R <=> P∨(Q ∨ R)

(P ∧ Q) ∧ R <=> P ∧ (Q ∧ R)

3) Commutative Law

( P ∧ Q) <=> (Q ∧ P)

( P ∨ Q) <=> (Q ∨ P)

4) Distributive Law

P ∨ (Q ∧ R) <=> (P ∨ Q) ∧ (P ∨ R)

P ∧ (Q ∨ R) <=> (P ∧ Q) ∨ (P ∧ R)

5) Identity Laws

(P ∧ T) <=> P

(P ∨ F) <=> P

6) Domination Law

(P ∨ T) <=> T

(P ∧ F) <=> F

7) Negation Law

¬(¬P) <=> P

8) Demorgan’s Law

¬(P ∧ Q) <=> ¬P ∨ ¬Q

¬(P ∨ Q) <=> ¬P ∧ ¬Q

9) Absorption Law

P ∨ (P ∧ Q) <=> P

P ∧ (P ∨ Q) <=> P

Some other equivalence formulas

P -> Q <=> ¬P ∨ Q

P -> Q <=> ¬Q -> ¬P

P <-> Q <=> (P ∧ Q) ∨ (¬P ∧ ¬Q)

P <-> Q <=> (P -> Q) ∧ (Q -> P)

¬(P <-> Q) <=> P <-> ¬Q