A proposition is a statement that is either TRUE or FALSE. It is the fundamental atom of logic -- indivisible, unambiguous, binary.

In this forest, each proposition is a single glowing tree. It stands lit or dark, alive or dormant. There is no middle state.

The NOT gate inverts. What was TRUE becomes FALSE. The mirror pool reflects everything reversed -- trees become roots, day becomes night.

The AND gate requires both paths to be open. Two mossy stone archways merge into one. A pixel deer can only pass through if both arches stand clear.

P AND Q = TRUE only when P = TRUE and Q = TRUE

The OR gate opens when either path carries flow. A forked river runs if rain falls on one branch, the other, or both.

P OR Q = TRUE when at least one input is TRUE

The XOR gate is the mushroom ring -- only one may glow. If both glow simultaneously, both extinguish. One or the other, never both.

P XOR Q = TRUE when exactly one input is TRUE

If the sun rises, then the forest wakes. Implication is false only when the premise is true but the conclusion is false. A promise broken.

P IMPLIES Q = FALSE only when P = TRUE and Q = FALSE

Two trees grow in perfect symmetry. If both glow or both dim, the gate opens. The biconditional is true when both sides agree.

P IFF Q = TRUE when P and Q have the same truth value