Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 122 — #130
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Chapter 4
Mathematical Data Types
Class Problems
Problem 4.36.
Let A D fa 0 ; a 1 ; : : : ; a n 1 g be a set of size n, and B D fb 0 ; b 1 ; : : : ; b m 1 g a set
of size m. Prove that jA Bj D mn by defining a simple bijection from A B to
the nonnegative integers from 0 to mn 1.
Problem 4.37.
Let R W A ! B be a binary relation. Use an arrow counting argument to prove the
following generalization of the Mapping Rule 1.
Lemma. If R is a function, and X A, then
jXj jR.X/j: