Math 213 - Homework 10
Assigned: 10/24/07
Due: 10/31/07 at the start of class.
Notation: Exercise a.b.c(d) stands for part (d) of Exercise c from Section a.b.
Problems:
(1) 8.1.4(a).
(2) 8.1.6(d).
(3) 8.1.54(a).
(4) 8.3.8. (Irreflexive is defined after problem 8.1.8 on pg. 526)
(5) 8.3.22.
(6) Show that the relation coming from a tournament is antisymmetric.
(7) 8.5.12. How many equivalence classes are there?
(8) 8.5.16.
(9) Suppose that mis a positive integer. Suppose that a1,a2,b1, and b2are positive integers
with a1≡b1(mod m), and a2≡b2(mod m). Show that a1+a2≡b1+b2(mod m)
and a1a2≡b1b2(mod m).
(10) Let A={(a, b)∈R|one of aor bis nonzero }. Define a relation on Aby saying that
(a, b) is related to (c, d) if and only if ax +by = 0 and cx +dy = 0 are the same line.
Show that this is an equivalent relation.
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