Formal reasoning lives here as marker doodles, wobbly diagrams, soft bubbles, and tiny proofs that flip open like notebook pages.
Click any card to turn it over. Some backs contain exercises; others contain the professor's margin notes and miniature truth machines.
A proposition is any sentence that can settle into True or False.
P: the moon hums
Questions, commands, and exclamations are dramatic, but they are not propositions until they can be evaluated.
This bubble is false.
A tiny contradiction rattles against the glass.
Self-reference can make truth values chase their own tails, which is why formal systems draw careful borders.
Both inputs must glow for the result to glow.
One bright input is enough to wake the output.
A ∨ B is true when A, B, or both are true.
The inverter turns True into False and False into True.
¬¬P ≡ P
Two flips bring the doodle back home.
Exactly one side gets to wear the glowing hat.
Same inputs: False. Different inputs: True. XOR is a little fairness referee.
¬(A ∧ B) ≡ ¬A ∨ ¬B
¬(A ∨ B) ≡ ¬A ∧ ¬B
Push negation through parentheses and the connective changes costume.
If the promise exists and the condition arrives, the conclusion may step forward.
Branches are reasons. Leaves are claims. The root is the rule that lets the tree bloom.
Sets overlap like transparent aurora puddles.
Union colors everything in either circle. Intersection colors only the shared middle.
Assume the opposite, follow the lines, and watch impossible sparks reveal the truth.
All cats are logicians. Mira is a cat. Therefore Mira is a logician.
The shared term connects the premises, like a bridge drawn between two islands.
The notebook is waiting for a proposition.
Complete A ∧ B
Four bubbles hide the outputs.