Bfh-sts: Created page with "= Contraposition = Contraposition is a transformation of an implication that produces a logically equivalent statement by reversing and negating its components. == Statement == * p → q ≡ ¬q → ¬p == Explanation == The implication "If p, then q" is equivalent to "If not q, then not p". This is often used in mathematical proofs. == Example == * "If it rains, then the ground is wet" ≡ "If the ground is not wet, then it does not rain". == Truth Table == {..."

2025-10-20T13:32:11Z

Created page with "= Contraposition = Contraposition is a transformation of an implication that produces a logically equivalent statement by reversing and negating its components. == Statement == * p → q ≡ ¬q → ¬p == Explanation == The implication "If p, then q" is equivalent to "If not q, then not p". This is often used in mathematical proofs. == Example == * "If it rains, then the ground is wet" ≡ "If the ground is not wet, then it does not rain". == Truth Table == {..."

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= Contraposition =

Contraposition is a transformation of an implication that produces a logically equivalent statement by reversing and negating its components.

== Statement ==
* p → q ≡ ¬q → ¬p

== Explanation ==
The implication "If p, then q" is equivalent to "If not q, then not p".
This is often used in mathematical proofs.

== Example ==
* "If it rains, then the ground is wet"
≡ "If the ground is not wet, then it does not rain".

== Truth Table ==
{| class="wikitable"
! p !! q !! p → q !! ¬q → ¬p
|-
| 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]]

Contraposition - Revision history