MAT 230 EXAM
ONE
1
0
y
x
Directions:
Type
your
solutions
into
this
document
and
be
sure
to
show
all
steps
for
arriving
at
your
solution.
Just
giving
a
final
number
may
not
receive
full
credit.
P
ROBLEM
1
(a)
The
domain
for
all
variables
in
the
expressions
below
is
the
set
of
real
numbers.
Determine
whether
each
statement
is
true
or
false.
(i)
∀
x
∃
y
(x
+
y
≥
0)
For
all
values
of
x,
there
exists
at
least
one
y
where
x
+
y
≥
0
is
true.
(ii)
∃
x
∀
y
(x
·
y
>
0)
There
a
exists
at
least
one
a
x
a
for
a
all
a
the
a
values
a
of
y
where
a
x
a
∗
a
y > 0.
If
y
=
0,
then
x
is
1
,
not
real
and
false.
(b)
Translate
each
of
the
following
English
statements
into
logical
expressions.
(i)
There
are
two
numbers
whose
ratio
is
less
than
1.
∃
x
∃
y
(
x
<
1)
(ii)
The
reciprocal
of
