AND
∧
Conjunction. Hexagonal sapphire. Both must shine.
Logic, Bedazzled.
The AND-gate, set in faceted sapphire. A conjunction holds only when every premise gleams. Lose one, lose all — the gem dims. The brilliance of p ∧ q is that it withholds nothing and forgives nothing.
An OR-gate, cut as a rounded diamond — generous, accommodating, almost flirtatious. p ∨ q asks for the slightest spark of truth and rewards it with the whole gleam. Inclusivity is its facet.
The NOT-gate flipped on its head — a chrome-tipped pyramid that reverses every truth it touches. ¬p is the smirk in the proof, the sequin that catches you off-guard. What you said? Now the opposite. Mounted.
Implication, in two-tier setting: antecedent above, consequent dangling like a chrome charm. p → q promises only that q never lies when p tells the truth. False premises absolve all sins — the McBling get-out clause.
Eight cuts of formal reasoning, mounted on velvet midnight.
∧
Conjunction. Hexagonal sapphire. Both must shine.
∨
Disjunction. Diamond cut. One spark suffices.
¬
Negation. Inverted pyramid. Mirrors every facet.
→
Implication. Two-tier mount. Antecedent above.
↔
Biconditional. Mirror-cut. Truths trade places.
∀
Universal. Tiara of trues. None excluded.
∃
Existential. Solitaire setting. One witness, please.
⊢
Turnstile. Engraved hallmark. The seal of validity.