Let A=ia1 + ja2 + ka3
B= ib1 +jb2 =kb3 and
C=ic1 + jc2 +kc3
B.C =b1c1 + b2c2 +b3c3 is a scaler and so
A.(B.C) = (b1c1 + b2c2 +b3c3)(ia1 +ja2 +ka3)
A.(B.C) = ia1b1c1 +ja2b2c2 +ka3b3c3 . . . . . . . . . . .(1)
A.B = a1b1 + a2b2 +a3c3 is a scaler and
(A.B).C = (a1b1 + a2b2 +a3c3)(ic1 + jc2 +kc3)
(A.B).C = ia1b1c1 + ja2b2c2 + ka3b3c3 . . . . . . . . . . (2)
RHS’s of (1) and (2) are identical and so
the LHS’s should be equal and hence it follows that
A.(B.C) = (A.B).C
1) Juan and Sofia doubt that
2) lili and don jose are not likely
3) the sports club denies that
4) it is not possible that antonio and mauricio
5) Doña Lucia does not believe that
6) it is impossible that pedrito and you take
7) Felipe and Sister Piedad are not sure that
8) it is impossible that Guillermina and Jorge
9) it is not true that lili and sofia
10) it is not true that the sports club
11) it is not certain that don josé and juan
12) doña lucia and guillermina do not believe that
Ñ and N i think if not try M
Hint : what is established is what is there. Since you need 16 letters, we will use it in plural, establishments.
Answer : Establecimientos.
Hope this helps!
