Touch logic. Break it. Rebuild it.
This sentence is false. If it is true, then it is false. If it is false, then it is true. A self-referential loop that breaks classical logic.
Given: If it rains, the ground is wet. It is raining. Conclude: The ground is wet. The simplest valid deduction.
Complete the truth table for the expression: (P ∧ Q) → (P ∨ R). Consider all eight possible combinations of truth values for three variables.
How many rows evaluate to FALSE?
Consider the set of all sets that do not contain themselves. Does this set contain itself? A paradox that shook the foundations of mathematics.
Is it necessarily true that 2 + 2 = 4? What is the difference between something being true and something being necessarily true?
One grain of sand is not a heap. Adding one grain to a non-heap does not make it a heap. Therefore, no amount of sand is a heap.
Where does vagueness meet logic?
If P → Q, then ¬Q → ¬P. Always valid. The logical mirror of implication that reveals hidden structure.
¬(P ∧ Q) ≡ (¬P ∨ ¬Q). The negation of a conjunction is the disjunction of the negations. Elegant symmetry.