Bfh-sts: Created page with "= Implication = Implication is the logical operation corresponding to "IF ... THEN". It expresses that if one proposition holds, then another must also hold. == Symbols == * p → q (standard notation) * p ⊃ q (alternative) * IF p THEN q (verbal) == Definition == The implication ''p → q'' is false only when ''p'' is true and ''q'' is false. In all other cases it is true. Additionally, ''p → q'' can be reformed into ''¬ p ∨ q'' == Truth Table == {| class..."

2025-10-20T13:28:28Z

Created page with "= Implication = Implication is the logical operation corresponding to "IF ... THEN". It expresses that if one proposition holds, then another must also hold. == Symbols == * p → q (standard notation) * p ⊃ q (alternative) * IF p THEN q (verbal) == Definition == The implication ''p → q'' is false only when ''p'' is true and ''q'' is false. In all other cases it is true. Additionally, ''p → q'' can be reformed into ''¬ p ∨ q'' == Truth Table == {| class..."

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= Implication =

Implication is the logical operation corresponding to "IF ... THEN".
It expresses that if one proposition holds, then another must also hold.

== Symbols ==
* p → q (standard notation)
* p ⊃ q (alternative)
* IF p THEN q (verbal)

== Definition ==
The implication ''p → q'' is false only when ''p'' is true and ''q'' is false.
In all other cases it is true.

Additionally, ''p → q'' can be reformed into ''¬ p ∨ q''

== Truth Table ==
{| class="wikitable"
! p !! q !! p → q
|-
| T || T || T
|-
| T || F || F
|-
| F || T || T
|-
| F || F || T
|}

== Examples ==
* If ''p'' = "It rains" and ''q'' = "The ground is wet",
then ''p → q'' = "If it rains, then the ground is wet".
* In programming, implications are usually built using combinations of operators, e.g. in Python: <code>(not p) or q</code>.

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

Implication - Revision history