ece108: day 1 update

docs/1b/ece108.md

@@ -1,3 +1,63 @@
 # ECE 108: Discrete Math 1
 
+An **axiom** is a defined core assumption held to be true.
+
+!!! example
+    True is not false.
+
+A **theorem** is a true statement derived from axioms via logic or other theorems.
+
+!!! example
+    True or false is true.
+
+A **proposition/statement** must be able to have the property that it is exclusively true or false.
+
+!!! example
+    The square root of 2 is a rational number.
+
+An **open sentence** becomes a proposition if a value is assigned to the variable.
+
+!!! example
+    $x^2-x\geq 0$
+
 ## Truth tables
+
+A truth table lists all possible **truth values** of a proposition, containing independent **statement variables**.
+
+!!! example
+    | p | q | p and q |
+    | --- | --- | --- |
+    | T | T | T |
+    | T | F | F |
+    | F | T | F |
+    | F | F | F |
+
+## Logical operators
+
+!!! definition
+    - A **compound statement** is composed of **component statements** joined by logical operators AND and OR.
+
+The **negation** operator is equivalent to logical **NOT**.
+
+$$\neg p$$
+
+The **conjunction** operaetor is equivalent to logical **AND**.
+
+$$p\wedge q$$
+
+The **disjunction** operator is equivalent to logical **OR**.
+
+$$p\vee q$$
+
+The **implication** sign requires that if $p$ is true, $q$ is true, such that *$p$ implies $q$*. The first symbol is the **hypothesis** and the second symbol is the **conclusion**.
+
+$$p\implies q$$
+
+| $p$ | $q$ | $p\implies q$ |
+| --- | --- | --- |
+| T | T | T |
+| T | F | F |
+| F | T | T |
+| F | F | F |
+
+