Update eidma.md

Signed-off-by: Abdulkadir Furkan Şanlı <abdulocracy@disroot.org>

content/posts/eidma.md

@@ -179,3 +179,22 @@ markup = "pandoc"
       - Fact: $f^{-1}$ is a function iff $f$ is a *bijection* (1 to 1 and onto)
 
 - For some set $\mathbb A$ the image of $\mathbb A$ by $f$ is $f(\mathbb A) = \{ f(x) : x \in \mathbb A \}$. We can also define the inverse of an image even when the function itself isn't invertible: $f^{-1}(\mathbb A)$
+
+## Combinatorics
+
+- $|\mathbb A|$ size (number of elements) of $\mathbb A$
+- Rule of addition:
+  - If $\mathbb A, \mathbb B \subseteq \mathbb X$ and $|\mathbb A|, |\mathbb B| \in \mathbb N$ and $\mathbb A \cap \mathbb B = \emptyset$ then $|\mathbb A \cup \mathbb B| = |\mathbb A| + |\mathbb B|$
+  - Can be generalized as:
+$$
+(\forall n ) \mathbb{A}_1, \mathbb{A}_2, ..., \mathbb{A}_n \in \mathbb{X} \land \\
+|\mathbb{A}_1|, |\mathbb{A}_2|, ..., |\mathbb{A}_n| \in \mathbb{N} \implies \\
+(\forall i, j \in \{1, 2, ..., n \})(i \neq j \implies \mathbb{A}_i \cap \mathbb{A}_j = \emptyset)
+$$
+- Rule of multiplication:
+  - $\mathbb{A}, \mathbb{B} \subseteq \mathbb{X}, |\mathbb{A} \times \mathbb{B}| = |\mathbb{A}| \cdot |\mathbb{B}|$
+  - Can be generalized as:
+$$
+(\forall n ) \mathbb{A}_1, \mathbb{A}_2, ..., \mathbb{A}_n \in \mathbb{X} \land |\mathbb{A}_i| \in \mathbb{N} \implies \\
+|\mathbb{A}_1 \times \mathbb{A}_2 \times ... \times \mathbb{A}_n| = |\mathbb{A}_1| \cdot |\mathbb{A}_2| \cdot ... \cdot |\mathbb{A_n}|
+$$