| Phi 270 Fall 2013 |
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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 separated 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 separated 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 separated 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 separated 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 separated 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 separated 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 |