Bfh-sts: Created page with "= Distributive laws = The distributive laws describe how conjunction and disjunction distribute over each other. They show that a conjunction can be distributed over a disjunction, and a disjunction can be distributed over a conjunction. == Statements == * p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r) * p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r) == Explanation == These rules are similar to the distributive property in arithmetic. They allow logical formulas to be r..."

2025-10-20T13:30:15Z

Created page with "= Distributive laws = The distributive laws describe how conjunction and disjunction distribute over each other. They show that a conjunction can be distributed over a disjunction, and a disjunction can be distributed over a conjunction. == Statements == * p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r) * p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r) == Explanation == These rules are similar to the distributive property in arithmetic. They allow logical formulas to be r..."

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= Distributive laws =

The distributive laws describe how conjunction and disjunction distribute over each other.
They show that a conjunction can be distributed over a disjunction, and a disjunction can be distributed over a conjunction.

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

== Explanation ==
These rules are similar to the distributive property in arithmetic.
They allow logical formulas to be rewritten in different but equivalent forms.

== Examples ==
* "I study AND (I pass OR I fail)" is equivalent to "(I study AND I pass) OR (I study AND I fail)".
* "I travel OR (I save money AND I rest)" is equivalent to "(I travel OR I save money) AND (I travel OR I rest)".

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

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

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

Distributive laws - Revision history