Rob Bayer
Math 55 MT1 Review
July 8, 2009
Instructions
•
Work through the following review problems as a group
•
Make sure to focus not just on getting the correct answers, but also on how you would actually write your
proofs/solutions
•
Feel free to skip around–there’s way more problems here than the actual midterm will have, so focus on
whatever your group wants practice with.
•
As always with review/practice tests, the inclusion or exclusion of certain topics should not be taken as an
indication of what will be on the actual midterm.
Logic and Proof Techniques
1. Write a truth table for the compount proposition (
p
→
q
)
∨
(
q
∧
r
)
→
r
2. Determine whether each of the following are true or false. The domain for all variables is the set of nonnegative
integers. Justify your answers.
(a)
∀
x
∃
y
(
y > x
)
(b)
∀
x
∀
y
(
x
2
+
y
2
≥
2
xy
)
(c)
∃
x
∀
y
((
∃
z x
=
yz
)
→
(
z
= 1
∨
y
= 1))
(d)
∃
x
∀
y
(
x
6
=
y
)
3. Without using a truth table, show that (
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 Summer '08
 STRAIN
 Math, Negative and nonnegative numbers, actual midterm, Rob Bayer, MT1 Review

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