@pmalynin, you forgot the safety variable.

  p | q | p ∧ q → ¬q
  --+---+-----------
  T | T | F         You can't be safe and own a gun.
  T | F | T         You can be safe and not own a gun.
  F | T | T         You can be unsafe and own a gun.
  F | F | T         You can be unsafe and not own a gun.

@rwjwjuwjudf, logical implication is correct - logical equivalence leads to this trainwreck:

  p | q | p ∧ q ↔ ¬q
  --+---+-----------
  T | T | F         You can't be safe and own a gun.
  T | F | F         You can't be safe and not own a gun.
  F | T | T         You can be unsafe and own a gun.
  F | F | F         You can't be unsafe and not own a gun.