1.4.xa. Exercise answers

1. a. (i) The set consisting of The gizmo is a widget and The gizmo is a gadget cannot be divided from the empty set; that is, (ii) there is no possibility of the gizmo being both a widget and a gadget.
  b. (i) The empty set cannot be divided from the set consisting of The gizmo is a widget and The gizmo is a gadget; that is, (ii) there is no possibility of the gizmo being neither a widget nor a gadget
  c. (i) The empty set cannot be divided from the set consisting of only The widget plinked; that is, (ii) there is no possibility that the widget did not plink
  d. (i) The set consisting of only The widget plonked cannot be divided from the empty set; that is, (ii) there is no possibility that the widget plonked
  e. (i) The set consisting of only The widget was a gadget cannot be divided from the set consisting of The widget plinked and The widget plonked; that is, (ii) there is no possbility that the widget was a gadget while not either plinking or plonking.
  f. (i) The set consisting of The widget was a gizmo, The widget plinked, and The widget plonked cannot be divided from the empty set; that is, (ii) there is no possibility that the widget was a gizmo and both plinked and plonked
2. a. The gadget is red entails The gadget is not green (or: The gadget is green entails The gadget is not red)
  b. The auditorium is empty entails There are empty seats in the auditorium (or: There are no empty seats in the auditorium entails The auditorium is not empty)
  c. A widget is a not widget is absurd
  d. A widget is a not gadget is a tautology
  e. The widget is a gadget or gizmo, The widget is not a gadget, and The widget is not a gizmo are inconsistent
  f. The widget has not finished the task and The widget has not broken render exhaustive The widget has not advanced and The widget has not plonked
Glen Helman 01 Aug 2011