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104
TULSI-PRAJNA
or al bial b2 al 13 a2 b1 a2 b2 a2 63 This is equivalent to the cartesion product of A and B. AXB=[(al, b1), (al, 62), (a1, 63), (a2, bl), (a2. 62), (a2, (63) ] Again cover each one of these ordered pairs with C. (a1 b1)* (al b2)(al 63) (a2 61)c (a2 b2) (a2 b3). or albici, alb1c2, alb2c1, alb2c2, alb3c1, alb3c2
a2b1cl, a2b1c2, a2b2cl, a2b2c2, a2b3c1, a2b3c2 This is equivalent to the cartesion product of (AXB) and C. (AxB) x C=[(al,b1.cl), (a1.b1,c2). (a1,b2.ci), (a1,b2.c2)
(a1.b3.ci). (a1.63.c2). (a2.b1.cl), (a2.b1.c2)
(a2,b2.c1), (a 2,b2,c2), a2,63,cl). (a2,63,c2) (1.2) Second Prastara :
णिक्खित्तु विदियमेनं, पढ़म तस्सुवरि विदियमेक्केक्कं । पिंडं पडि णिक्खेओ, एवं सत्वत्थ कायव्वो ॥
The Gatha, in particular, says to place the elements of the first Pramada as many times as there are the elements in the second one and keep one by one the element of the second Pramada on the top of each element of the first one. Do like this in all Pramada.
This Gatha, in general, says to place the first set as many times as the number of the elements in the second one and then keep one by one the element of the second set on the top of each first one. Again place the set just obtained as many times as the number of the elements in the third set and keep one by one the element of the third set on the top of each placed one. Do this process till the last set.5
A
Example : Place A as many times as the number of the elements in B. A A
A Keep one by one the element of B on the top of each A.
bi 62 A
63 A
A or albi a2bi alb2a2b2 alb3a2b3 This is equivalent to the cartesion product of A and B. AxB= [(al, 61). (a2, b1), (al, 62), (a2, b2), (al, b3), (a2, 63) ] Again keep one by one the element of C on the top of each set just obtained after placing as many times as the number of the elements in C. (albl a2b1 alb2 a2b2 alb3 a2b3jol (albl a2b2 alb2 a2b2 alb3 a 263) or albicl, a2b1cl, alb2c1, a2b2cl, alb3c1, a2b3c1
albic2, a2b1c2, alb2c2, a2b2c2, alb3c2, a2b3c2
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