Discrete Mathematic Important formulas {Part 1}
1. Cumulative Law
p∧=∧ qqp pqqp ∨=∨
2. Associative Law
( ) () p∧ ∧= ∧ ∧ q r p qr ( ) () p∨ ∨= ∨ ∨ q r p qr
3. Distributive Law
p∧∨= ∧∨ ∧ ( )( )( ) qr pq pr p∨∧= ∨∧ ∨ ( )( )( ) qr pq pr
4. Idempotent Law
ppp ∧ = p∨ =p p
5. De-Morgans Law
~( ) ~ ~ p∧= ∨ q pp ~( ) ~ ~ p∨= ∧ q pp
6. Absorption Law
p∨∧= ( ) pq p p∧∨= ( ) pq p
7. Identity Law
p∧t p = pc p ∨ =
8. Universal Bond Law
p∨ =t t pcc ∧ =
9. Negation Law
p∨ = ~ p t (Tautology) p pc ∧~ = (Contradiction)
10. Negation of t and c ~t c = ~ c t =
11. Double Negation Law ~ (~ ) p = p
2.Set Identities:
Let A,B, and C be subsets of a Universal set U. then
1. Idempotent Law:
1. Cumulative Law
p∧=∧ qqp pqqp ∨=∨
2. Associative Law
( ) () p∧ ∧= ∧ ∧ q r p qr ( ) () p∨ ∨= ∨ ∨ q r p qr
3. Distributive Law
p∧∨= ∧∨ ∧ ( )( )( ) qr pq pr p∨∧= ∨∧ ∨ ( )( )( ) qr pq pr
4. Idempotent Law
ppp ∧ = p∨ =p p
5. De-Morgans Law
~( ) ~ ~ p∧= ∨ q pp ~( ) ~ ~ p∨= ∧ q pp
6. Absorption Law
p∨∧= ( ) pq p p∧∨= ( ) pq p
7. Identity Law
p∧t p = pc p ∨ =
8. Universal Bond Law
p∨ =t t pcc ∧ =
9. Negation Law
p∨ = ~ p t (Tautology) p pc ∧~ = (Contradiction)
10. Negation of t and c ~t c = ~ c t =
11. Double Negation Law ~ (~ ) p = p
2.Set Identities:
Let A,B, and C be subsets of a Universal set U. then
1. Idempotent Law:
