Logic

• What Is the Truth Value of P(x,y,z)?
  The predicate P(x,y,z) is true exactly when x+y is at most z, but the missing expression is needed to determine the requested truth value.
• How to Find the Million-Dollar Door with One Question
  With two doors and one truthful guard and one liar, ask either guard which door the other would name, then choose the opposite door.
• Disprove the Claim That All Birds Can Fly
  Disprove “all birds can fly” with a counterexample: penguins are birds but cannot fly through the air. See the matching logic in predicate form.
• How Does a Chain of Implications Prove Conditions Equivalent?
  A chain proves several conditions equivalent when its implications connect every condition and eventually return to the starting one.
• How to Build a Logic Circuit in Conway’s Game of Life
  Conway’s Game of Life can compute with moving patterns such as gliders; design a Boolean circuit first, then implement and test its signal interactions.
• How Do Brackets Work in Boolean Algebra’s Distributive Laws?
  Learn how parentheses group Boolean expressions, when to distribute AND or OR, and how to simplify bracketed expressions without changing their value.
• How to Prove (∀x P(x) → A) → ∃x(P(x) → A)
  A classical proof uses cases on A and requires a nonempty domain; the statement is not generally valid in intuitionistic logic.
• How Much Did the Shop Lose in the Stolen-Money Riddle?
  In the classic stolen-money riddle, the shop loses $100 at selling price: $70 in goods and $30 in change, not $200.