Bfh-sts: Created page with "= Associative laws = The associative laws state that when combining three or more propositions with conjunction or disjunction, the grouping of the operations does not affect the truth value. == Statements == * (p ∧ q) ∧ r ≡ p ∧ (q ∧ r) * (p ∨ q) ∨ r ≡ p ∨ (q ∨ r) == Explanation == Parentheses can be rearranged without changing the logical meaning. == Examples == * "((I study AND I practice) AND I succeed)" is equivalent to "(I study AND (I practi..."

2025-10-20T13:30:00Z

Created page with "= Associative laws = The associative laws state that when combining three or more propositions with conjunction or disjunction, the grouping of the operations does not affect the truth value. == Statements == * (p ∧ q) ∧ r ≡ p ∧ (q ∧ r) * (p ∨ q) ∨ r ≡ p ∨ (q ∨ r) == Explanation == Parentheses can be rearranged without changing the logical meaning. == Examples == * "((I study AND I practice) AND I succeed)" is equivalent to "(I study AND (I practi..."

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= Associative laws =

The associative laws state that when combining three or more propositions with conjunction or disjunction, the grouping of the operations does not affect the truth value.

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

== Explanation ==
Parentheses can be rearranged without changing the logical meaning.

== Examples ==
* "((I study AND I practice) AND I succeed)" is equivalent to "(I study AND (I practice AND I succeed))".
* "((It rains OR it snows) OR it is windy)" is equivalent to "(It rains OR (it snows OR it is windy))".

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

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

Associative laws - Revision history