Set Theory
Membership, unions, intersections, infinity, and the foundational language of mathematical collections.
Formal Sciences
[ DOMAIN 02 ]
LOGIC
The architecture of truth. Logic strips away context, emotion, and bias, leaving only the immutable framework of valid reasoning.
Level 1: Binary States & Connectives
Before we can build complex mathematical proofs or computer algorithms, we must define the absolute basics: True and False. At this level, we only care about how simple statements combine together.
∧
AND
∨
OR
¬
NOT
The Truth Engine
Variables
2-BIT
# Binary Connectives
AND
∧
0∧0
=
0
State
FALSE
OR
∨
0∨0
=
0
State
FALSE
XOR
Exclusive
⊕
0⊕0
=
0
State
FALSE
NAND
Not AND
⊼
0⊼0
=
1
State
TRUE
IMPLIES
If P, then Q
⇒
0⇒0
=
1
State
TRUE
IFF
Biconditional
⇔
0⇔0
=
1
State
TRUE
Module: Propositional Logic
Boolean connectives, truth tables, implication, equivalence, and the algebra of true and false statements.
Level 2: Quantifiers & Sets
Simple true/false statements aren't enough to describe the universe. "All dogs are mammals" requires a new syntax. Here, we introduce Quantifiers and begin grouping objects into overlapping Sets.
Set & Quantifier Visualizer
Module_02 // Interactive
The Universe (U)
Set A
(Circles)
(Circles)
Set B
(Filled)
(Filled)
Notice how a single counter-example breaks a Universal (∀) statement. If you say "∀ objects in Set B are Filled", the engine immediately flags the empty circles as the reason the statement is FALSE.
Level 3: Informal Logic
Mathematical logic is perfect. Humans are not. When we attempt to apply logical structures to everyday language and debate, we frequently make structural errors known as Logical Fallacies.
Module: Cognitive Biases & Fallacies
Common structural failures in everyday reasoning, including ad hominem, straw-man arguments, and related fallacies.
[ Q.E.D. VERIFICATION ]
Proof of Comprehension1 / 5