From 7bb5984746f00bc1b2007230530853439e434955 Mon Sep 17 00:00:00 2001 From: eggy Date: Wed, 11 Jan 2023 13:30:32 -0500 Subject: [PATCH] ece108: complete converse contrapositive --- docs/1b/ece108.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/docs/1b/ece108.md b/docs/1b/ece108.md index 042515d..dcf417e 100644 --- a/docs/1b/ece108.md +++ b/docs/1b/ece108.md @@ -111,3 +111,11 @@ $$ An implication can be expressed as a disjunction. As long as it is stated, it can used as its definition. $$p\implies \equiv (\neg p)\vee q$$ + +Two **converse** propositions imply each other: + +$$p\implies q\text{ is the converse of }q\implies p$$ + +A **contrapositive** is the negatated converse, and is **logically equivalent to the original implication**. This allows proof by contrapositive. + +$$\neg p\implies\neg q\text{ is the contrapositive of }q\implies p$$