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O'Reilly Platform
book
The Nuts and Bolts of Proofs, 4th Edition
by
Antonella Cupillari
January 2011
Beginner content level
Beginner
296 pages
11h 43m
English
Academic Press
Content preview from
The Nuts and Bolts of Proofs, 4th Edition
More
about
Equivalence
Relations
Equivalence
relations
have
three
strong
prop erties,
and
they
define
strong
ties
between
the
elements
of
a
set.
The
elements
that
are
in
relation
with
each
other
can
all
be
grouped
in
a
special
set,
called
an
equiva-
lence
class.
Let
’
s
examine
the
precise
definition
of
these
sets .
Let
A
be
a
set
and
R
an
equivalence
relation
defined
on
A
.
Let
x
∈
A
.If
xRy
,
the
ele ments
x
and
y
are
said
to
be
equivalent
.
The
equivalence
class
of
x
determined
by
R
is
the
set
½
x
=
f
a
∈
A
j
aRx
g
:
EXAMPLE
4.3.11
Consider
again
the
relation
in
Example
4.3.8
,
where
A
=
{1,
2,
3,
4}
and
the
relation
is
aRb
if
and
only
if
a
−
b
is
an
even
number ...
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Publisher Resources
ISBN: 9780123822178