From d75d56f323ef432d0181efb45e7afec7a14be248 Mon Sep 17 00:00:00 2001 From: Avi Date: Sun, 15 Sep 2024 14:12:08 +0000 Subject: [PATCH] minor update --- math/logic/README.md | 22 +++++++++++++--------- 1 file changed, 13 insertions(+), 9 deletions(-) diff --git a/math/logic/README.md b/math/logic/README.md index 341daf2..0c7ce2f 100644 --- a/math/logic/README.md +++ b/math/logic/README.md @@ -26,7 +26,7 @@ Read: Discrete Mathematics and Its Applications by Kenneth H. Rosen (not require - We studied sentential logic as part of the course, but it is often referred to as Propositional logic/calculus -- We also used a system called L arrow which exists in sentential logic (sometimes called language PC) +- We also used a system called L arrow which exists in sentential logic - I advise reading the Rosen Discrete Math Book, in the first few hundred pages... it covers most of what the course does. @@ -52,14 +52,18 @@ Here are some stuff worth knowing (on top of the basic gates/symbols) - When A is true and B is false, the sentence gets the False truth value, otherwise it will always get the True truth value - - Called If then, implies, or conditional + - Called If then, Implies, or Conditional * A ↔ B = A ⊙ B ≡ (A ⇒ B) ∧ (B ⇒ A) - - if and only if = xnor + - if and only if = x-nor * A ⊕ B ≡ (A ∧ ¬B) ∨ (¬A ∧ B) + * ∀y - Universal quantifier - For all y + + * ∃x - Existential quantifier - There exists x + ### English to Logic |Sentential Logic Sentence|A ↔ B |A → B |~B → A |~(A → B) = A ∧ ~B |A ∧ B |A ∨ B |A ↑ B |A ↓ B |(A → B) & (~A → C) |(~B → A) & (B → C) | @@ -108,15 +112,15 @@ Here are some stuff worth knowing (on top of the basic gates/symbols) - OR, NOT : {∨, ¬} -- and here are some additional ones +- Additional ones: -- IMP, NOT : {⇒, ¬} + - IMP, NOT : {⇒, ¬} -- XOR, IMP : {⊕, ⇒} + - XOR, IMP : {⊕, ⇒} -- AND, BIDIRECTIONAL, FALSE : {∧, ↔, F} + - AND, BIDIRECTIONAL, FALSE : {∧, ↔, F} -- OR, BIDIRECTIONAL, FALSE : {∨, ↔, F} + - OR, BIDIRECTIONAL, FALSE : {∨, ↔, F} ## Graphs: @@ -247,7 +251,7 @@ Meta-implication: A ⊨ B ##### Terms you may see elsewhere -First order logic = Predicate logic (For all, There exists) +First order logic = Predicate logic/calculus (For all, There exists) * If A ⊢ B then A ⊨ B (soundness theorem)