View source for Neutral and dominance laws

= Absorption laws =

The absorption laws show how certain combinations of conjunction and disjunction can be simplified by "absorbing" one proposition into another.

== Statements ==
* p ∨ (p ∧ q) ≡ p
* p ∧ (p ∨ q) ≡ p

== Explanation ==
Adding extra conditions that are already implied by ''p'' does not change the truth value.  
These laws allow expressions to be reduced in complexity.

== Examples ==
* "I study OR (I study AND I rest)" is logically equivalent to "I study".
* "I study AND (I study OR I rest)" is logically equivalent to "I study".

== Truth Table (First Law) ==
{| class="wikitable"
! p !! q !! p ∧ q !! p ∨ (p ∧ q)
|-
| T || T || T || T
|-
| T || F || F || T
|-
| F || T || F || F
|-
| F || F || F || F
|}

== Truth Table (Second Law) ==
{| class="wikitable"
! p !! q !! p ∨ q !! p ∧ (p ∨ q)
|-
| T || T || T || T
|-
| T || F || T || T
|-
| F || T || T || F
|-
| F || F || F || F
|}

[[Category:Propositional logic (Aussagenlogik)]]
[[Category: Diskrete Mathematik I (BZG1155pa) 25/26]]