15.  Take any universal affirmative proposition; convert it by obversion (contraposition); attach the negative particle to the predicate, and again convert.  Interpret the result exactly, and say whether it is or is not equivalent to the original proposition. [S]

16.  What information about the term “solid body” can we derive from the proposition, “No bodies which are not solids are crystals”? [S]

17.  Discuss the proposal to treat all propositions as affirmative.

18.  Convert the proposition “A is probably B.”  What information does the proposition give us concerning B? [S]

19.  Show in how many ways you can deny the following assertions:  All cathedral towns are all cities; Canterbury is the Metropolitan see. [S]

20.  Explain the nature of a hypothetical (or conditional) proposition.  What do you consider the radical difference between it and a categorical? [S]

21.  What is the function of the copula?  In what different manners has it been treated? [S]

22.  Convert “A killed C unjustly”; “All Knowledge is probably useful”; “The exception proves the rule”; “Birds of a feather flock together.” [S]

23.  What is modality?  How are modals treated by (a) formal logic and (b) by the theory of induction? [S]

24.  What is the subject of an impersonal proposition?  Give reasons for your answer. [S]

25.  Is the categorical proposition sufficiently described as referring a thing or things to a class? [S]

26.  Enumerate the cases in which the truth or falsity of one proposition may be formally inferred from the truth or falsity of another.  Illustrate these cases, and give to each its technical name. [S]

27.  Illustrate the relation of Immediate Inferences to the Laws of Thought.

28.  Explain what is meant by (a) Symbolic Logic; (b) the Logic of Relatives.  Describe some method of representing propositions by means of diagrams; and indicate how far any particular theory of the import of propositions is involved in such representation. [S]

29.  Explain the exact nature of the relation between two Contradictory propositions; and define Conversion by Contraposition, determining what kind of propositions admit of such conversion.

Give the contradictory and the contrapositive of each of the following propositions:—­

    (a) All equilateral triangles are equiangular;

    (b) No vertebrate animal has jaws opening sideways;

    (c) Wherever A and B are both present, either C or D is also
    present. [S]

30.  Define Obversion and Inversion, and apply these processes also to the above three propositions.

31.  Propositions can be understood either in extension or in intension.  Explain this, and discuss the relative value of the two interpretations. [S]

32.  Distinguish between real and verbal propositions; and explain the importance of the distinction.