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Role of Space-Time in Jaina's Syàdväda
three. We shall show this by means of appropriate truth tables. (a) Let the EPM (Saw) = a) be denoted by a and the EP:M (S81) = b by B, i=1,2 .....n. In the case (a) we construct the following truth table 4.
Truth-Table 4 The truth values in the second and the seventh columns of the truth-table 4 show that the distributive law
a A (B, V B.) = (a AB.) V (a A B2) holds.
We now consider the case (b), where the operator A has the spectrum of two eigenvalues and B has also two. In this case we denote the EP's corresponding to the observable A as a, and A, and the EP's corresponding to the observable B as B, and B, the EP's Corresponding to the observables. For this case, we have the following truth-table 5.
Truth-Table 5 The truth values in the columns 4 and 12 in the truthtable 5 show that the distributive law holds. Finally, in the case (c) we denote the EP's corresponding to the observable A as a,,a, and an and the EP's corresponding to the observable B and B, B, and Bz. In this case we have the following truth-table 6.
Truth-Table 6 The truth values in the columns 8 and 19 in the truth-table 6 show that the distributive law holds even in this case. It is possible to construct truth tables for more complex cases involving more than three eigenvalues each and see that the distributive law holds in all these cases.
Secondly, we consider the other case of incompatible observable. Again, here we look into (a) Phas only one eigenvalue and Q has two, (b) P has 2 eigenvalues. Qhas also two and (c) P and 2 eigenvalues but Q has three. Let the EP:
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