102. How may the condition A .|. B = ACD •!• BCD
be expressed in four non-disjunctive equations ?

103. Verify the equivalence of M = Mn and N = Nw,

R 2



244 EQUATIONAL LOGIC. [chap.
when for M and N we substitute successively the following
pairs of values: —

r M = A, r M = A3,

^'M N = ABC. ^^^ I N = cD.
J M = ACD -I- A^^D .|. adCd,
(3) I N « dD H. Bed.
104. Express each of the following propositions equa-
tionally in a series of non-disjunctive propositions :

(i) Either the king is dead, or he is now on the march.
(2) Either compression or expansion will produce either
heat or cold in a solid body.
(3) A3 .|. 3C = C^ -I- cD.
(4) AB .1. AC = (AB .|. AC) (G/ -I- ^D).
105. In problem 20 (chap. xxi. p. 194) what description
should we obtain of the classes c, those who do not take
snuff, and d, those who do not use tobacco, respectively
under the several conditions (i), (2) and (3), with (4)?

106. In problem 29, pp. 200-1, draw descriptions of
the classes A^, ady and rD.
107. Represent symbolically the logical import of the
sentence : " If it be erroneous to suppose that all certainty
is mathematical, it is equally an error to imagine that all
which is mathematical is certain."

108. Represent equationally the logical import of this
extract from the Oath of Supremacy : " No foreign prince,
prelate, person, state, or potentate, hath any jurisdiction,
power, superiority, pre-eminence, or authority, ecclesiastical
or spiritual, within this realm." Observe especially how
far the alternatives are or are not mutually exclusive.
