DISJUNCTIVE PROPOSITIONS. 91 



alternative of the other. Since flowering plants are 

 either exogens or endogens, and are at the same time either 

 herbs, shrubs or trees, it follows that there are altogether 

 six alternatives namely, exogenous herbs, exogenous 

 shrubs, exogenous trees, endogenous herbs, endogenous 

 shrubs, endogenous trees. This process of combination is 

 shown in the general form 



(A ! B) (0 I- D) = AC ! AD * BC |- BD. 

 It is hardly necessary to point out that, however numerous 

 the terms combined, or the alternatives in those terms, we 

 may effect the combination provided each alternative is 

 combined with each alternative of the other terms, as in 

 the algebraic process of multiplication. 



Some processes of deduction may at once be exhibited. 

 We may always, for instance, unite the same qualifying 

 term to each side of an identity even though one or both 

 members of the identity be disjunctive. Thus let 



A = B|- C. 

 Now it is self-evident that 



AD = AD, 



and in one side of this identity we may for A substitute 

 its equivalent B -|- C obtaining 



AD = BD | CD. 



Since ' a gaseous element is either hydrogen, or oxygen, 

 or nitrogen, or chlorine, or fluorine/ it follows that ' a free 

 gaseous element is either free hydrogen, or free oxygen, 

 or free nitrogen, or free chlorine, or free fluorine.' 



This process of combination will lead to most useful 

 inferences when the qualifying adjective combined with 

 both sides of the proposition is a negative of one or more 

 alternatives. Since chlorine is a coloured gas, we may 

 infer that ' a colourless gaseous element is either (colour- 

 less) hydrogen, oxygen, nitrogen, or fluorine.' The alter- 

 native chlorine disappears because colourless chlorine does 

 not exist, Again, since 'a tooth is either an incisor, 



