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avipars authored Sep 15, 2024
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Expand Up @@ -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.

Expand All @@ -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) |
Expand Down Expand Up @@ -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:
Expand Down Expand Up @@ -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)

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