Any claim that a deductive relation holds can be stated as one or more claims that one set of sentences cannot be divided from another. (i) Restate each of the following claims in that way, and (ii) explicitly describe the sort of possibility that would divide the sets in question and is thus ruled out by claiming that the deductive relation holds. Nonsense words have been used to help you think to think how a possibility would be described without worrying whether that possibility could really occur.

For example, the claim that The widget plonked is equivalent to The widget plinked can be restated by saying that (i) the set consisting of the first sentence cannot be divided from the set consisting of the second sentence and vice versa. That is, (ii) it rules out any possibility in which the widget plonked but did not plink and any possibility in which the widget plinked but did not plonk.

The basic law for relative exhaustiveness can be used not only to replace alternatives by assumptions but also to replace assumptions by alternatives. For example, The widget is blue entails The widget is colored can be restated to say (i) The widget is blue and The widget is not colored are inconsistent, (ii) The widget is not blue and The widget is colored form an exhuastive set, and (iii) The widget is not colored entails The widget is not blue.

In the following, you will be asked to restate some statements of deductive relations by replacing alternatives with assumptions or assumptions with alternatives. You may add or remove ordinary negation to state the contradictories of sentences.