CHAP. XI.] OF SECONDARY PROPOSITIONS. 173 



In like manner the equations 



will respectively assert the truth and the falsehood of the disjunc- 

 tive Proposition, "Either X is true or Y is true." The equa- 

 tions 



y = vx 



y = v(l -x) 



will respectively express the Propositions, " If the proposition Y 

 is true, the proposition X is true." "If the proposition Y is 

 true, the proposition X is false." 



Examples will frequently present themselves, in the suc- 

 ceeding chapters of this work, of a case in which some terms of a 

 particular member of an equation are affected by the indefinite 

 symbol v, and others not so affected. The following instance 

 will serve for illustration. Suppose that we have 



y = xz + vx (1 - 2"). 



Here it is implied that the time for which the proposition Y is 

 true consists of all the time for which X and Z are together true, 

 together with an indefinite portion of the time for which X is 

 true and Z false. From this it may be seen, 1st, That if Yis 

 true, either X and ^are together true, or X is true and Z false ; 

 2ndly, If X and Z are together true, Y is true. The latter of 

 these may be called the reverse interpretation, and it consists in 

 taking the antecedent out of the second member, and the conse- 

 quent from the first member of the equation. The existence of 

 a term in the second member, whose coefficient is unity, renders 

 this latter mode of interpretation possible. The general principle 

 which it involves may be thus stated : 



14. PRINCIPLE. Any constituent term or terms in a particular 

 member of an equation which have for their coefficient unity, may 

 be taken as the antecedent of a proposition, of which all the terms 

 in the other member form the consequent. 



Thus the equation 



y = xz + vx (1 - z) + (1 - x) (1 - z) 

 would have the following interpretations : 



