Bfh-sts: Created page with "= Implication transformations = Implication can be expressed using other logical operators. These transformations allow ''p → q'' to be rewritten in equivalent forms. == Statements == * p → q ≡ ¬p ∨ q * ¬(p → q) ≡ p ∧ ¬q * p ↔ q ≡ (p → q) ∧ (q → p) == Explanation == * The implication ''p → q'' is equivalent to "not p or q". * The negation of ''p → q'' is equivalent to "p and not q". * Equivalence ''p ↔ q'' can be defined using tw..."

2025-10-20T13:31:58Z

Created page with "= Implication transformations = Implication can be expressed using other logical operators. These transformations allow ''p → q'' to be rewritten in equivalent forms. == Statements == * p → q ≡ ¬p ∨ q * ¬(p → q) ≡ p ∧ ¬q * p ↔ q ≡ (p → q) ∧ (q → p) == Explanation == * The implication ''p → q'' is equivalent to "not p or q". * The negation of ''p → q'' is equivalent to "p and not q". * Equivalence ''p ↔ q'' can be defined using tw..."

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= Implication transformations =

Implication can be expressed using other logical operators.
These transformations allow ''p → q'' to be rewritten in equivalent forms.

== Statements ==
* p → q ≡ ¬p ∨ q
* ¬(p → q) ≡ p ∧ ¬q
* p ↔ q ≡ (p → q) ∧ (q → p)

== Explanation ==
* The implication ''p → q'' is equivalent to "not p or q".
* The negation of ''p → q'' is equivalent to "p and not q".
* Equivalence ''p ↔ q'' can be defined using two implications.

== Examples ==
* "If it rains then the ground is wet"
≡ "Either it does not rain, or the ground is wet".
* "It is not the case that (if I study then I pass)"
≡ "I study and I do not pass".

== Truth Table (p → q ≡ ¬p ∨ q) ==
{| class="wikitable"
! p !! q !! p → q !! ¬p ∨ q
|-
| T || T || T || T
|-
| T || F || F || F
|-
| F || T || T || T
|-
| F || F || T || T
|}

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

Implication transformations - Revision history