Solutions to CS 390 Test II

April 9, 1998

1. tex2html_wrap_inline21
R(1,2,1) = a and R(2,2,1) = ba
Hence tex2html_wrap_inline27 .

2. Induction on tex2html_wrap_inline29 .
Basis Step: Since tex2html_wrap_inline31 and tex2html_wrap_inline33 , tex2html_wrap_inline35
Inductive Step: Assume that for an arbitrary tex2html_wrap_inline37 , tex2html_wrap_inline39 holds.
Then tex2html_wrap_inline41 by the definition of tex2html_wrap_inline43 since tex2html_wrap_inline39 .

Solutions to 3 and 4 are to be handed out in the class.


S. Toida
Thu Apr 9 18:05:30 EDT 1998