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{\large Math 1100 Core Algebra I}
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{\LARGE Term Test}
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University of Toronto, October 26, 2010
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\noindent{\bf Solve the 4 problems on the other side of this page. }\\
Each problem is worth 25 points.\\You have an hour and fifty minutes to
write this test.
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\noindent{\bf Notes.}
\begin{itemize}
\item No outside material other than stationary is allowed.
\item {\bf Neatness counts! Language counts!} The {\em ideal} written
solution to a problem looks like a page from a textbook; neat and clean
and made of complete and grammatical sentences. Definitely phrases like
``there exists'' or ``for every'' cannot be skipped. Lectures are mostly
made of spoken words, and so the blackboard part of proofs given
during lectures often omits or shortens key phrases. The ideal written
solution to a problem does not do that.
\item Advance apology: It may take us a while to grade this exam; sorry.
\end{itemize}
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\centerline{\bf Good Luck!}
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\noindent{\bf Solve the following 4 problems. } Each problem is worth
25 points. You have an hour and fifty minutes. {\bf Neatness counts!
Language counts!}
\vfill \noindent{\bf Problem 1. } Let $n$ be a natural number and let
$F$ be a subset of the set $\{(i,j)\colon 1\leq i