MAT 230 EXAM ONE
This document proprietary Southern New Hampshire University. the problems within is to It and
may not posted any non-SNHU website.be on
Jacqueline Amoah
1
then x is 1 , not real and false.
x
x
Directions: Type your solutions into this document and sure show all steps for arriving be to 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 true false.is or
(i)
∀
x
∃
y x (
+
y
≥
0)
For all values there exists of x, at least one y where
x +
y
≥
0 true.is
(ii)
∃
x
∀
y x (
·
y
>
0)
There exists least one x for all the values y where at of x
∗
y
>
0. If y
=
0,
0
(b)
Translate each following English statements into logical expressions.of the
(i)
There are two numbers whose ratio less than is 1.
∃
x
∃
y (
y
<
1)
(ii)
The reciprocal every positive number also positive.of is
∀
x (x
>
0
→
1
>
0)
P
ROBLEM
2
≤
· ≤
∗ ≤
∗ ≤
≥ ≥
Prove
the
following
using
the
specified
technique:
(a)
Let
x
and
y
be
two
real
numbers
such
that
x
+
y