56 Chapter 3
D6. The greatest integer function is discontinuous at every integer
because it has a jump discontinuity at every integer. On the
other hand it is continuous at every other real number because
it is a constant function on every open interval
Math 220 solutions- section 4.1, page 134
1. (a) Prove that division is a binary operation on R = R cfw_0.
Let x, y R and dene f : R R R by f (x, y) = x y = x/y. Then f is
a function and hence division is a binary operation.
(b) Prove that division on R i
66
Chapter 3
5.
Since a permutation is a bijection, Corollary 3.35 follows
immediately from part 3 of Proposition 3.3.4.
Converse of 1: If gf is surjective, then f is surjective and g is
surjective. This statement is false as we see from the following
Math 220 solutions- section 4.2, page 147
1. (a) Not reexive, not symmetric, transitive and anti-symmetric.
(b) Not reexive, not symmetric, not transitive, anti-symmetric.
(c) Not reexive, not symmetric, not transitive, anti-symmetric.
(d) Reexive, symmet