DISJUNCTIVE PROPOSITIONS. 89 



Various Forms of the Disjunctive Proposition. 



Disjunctive propositions may occur in a great variety of 

 forms, of which the old logicians took very insufficient 

 notice. There may be any number of alternatives each of 

 which may be a combination of any number of simple 

 terms, A proposition, again, may be disjunctive in one 

 or both members. The proposition 



Solids or liquids or gases are electrics or conductors of 



electricity 



is an example of the doubly disjunctive form. The mean- 

 ing of any such proposition is that whatever falls under 

 any one or more alternatives on one side must fall under 

 one or more alternatives on the other side. From what 

 has been said before, it is apparent that the proposition 



A | B = C | D 

 will correspond to 



ab = cd, 



each member of the latter being the negative of a 

 member of the former proposition. 



As an instance of a complex disjunctive proposition 

 I may give Senior's definition of wealth, namely * Wealth 

 is what is transferable, limited in supply, and either 

 productive of pleasure or preventive of pain s.' 

 Let A = wealth 



B == transferable 

 C = limited in supply 

 D = productive of pleasure 

 E = preventive of pain. 

 The definition takes the form 



A = BC(D! E); 



but if we develop the alternatives by a method to be 

 afterwards more fully considered, it becomes 

 A = BODE |- BCDe-h BCdE. 



8 Boole's 'Laws of Thought,' p. 106. Jevous' 'Pure Logic/ p. 69. 



