Tidy up and regenerate

content/posts/eidma.mmark

@@ -49,12 +49,13 @@ markup = "mmark"
 		- $$(p \implies q) \equiv (\neg p \lor q)$$
 		- $$(\neg q \implies \neg p) \equiv (\neg (\neg q) \lor (\neg p) \equiv (q \lor \neg p) \equiv (\neg p \lor q)$$
 
-	- Contradiction law:
-		- $$p \lor \neg p \equiv 1$$ and $$p \land \neg p \equiv 0$$
+- Contradiction law:
+	- $$p \lor \neg p \equiv 1$$ and $$p \land \neg p \equiv 0$$
 
 - Tautology: $$\phi (p, q, ... r)$$ is a tautology *iff* $$\phi \equiv 1$$
 
 ## Sets
+
 - We will consider subsets of universal set $$\mathbb X$$
 	- $$2^\mathbb X = \{ A : A \subseteq \mathbb X\}$$
 	- $$2^\mathbb X = P(\mathbb X)$$
@@ -84,12 +85,13 @@ markup = "mmark"
 - Quip: $$\{ x \in \mathbb R : x^2 = -1\} = \emptyset$$
 
 ## Quantifiers
+
 - $$\phi$$ - prepositional function: yields only true or false value
 - $$\forall$$ means "for all" and $$\exists$$ means "there exists"
-- $$\forall$$
+- $$\forall$$:
 	- Shorthand for $$\land$$ e.g. $$(\forall x \in \{ 1, 2, ... 10 \}) x > 0 \equiv 1 > 0 \land 2 > 0 \land ... 10 > 0$$
 
-- $$\exists$$
+- $$\exists$$:
 	- Shorthand for $$\lor$$ e.g. $$(\exists x \in \{ 1, 2, ... 10 \}) x > 5 \equiv 1 > 5 \lor 2 > 5 \lor ... 10 > 5$$
 
 - $$\neg \forall \equiv \exists$$, vice versa
@@ -106,6 +108,7 @@ markup = "mmark"
 - Order of quantifiers matters.
 
 ## Relations
+
 - Cartesian product:
 	- $$A \times B = \{ (p, q) : p \in A \land q \in B \}$$