Midterm 1, Math 55
July 16, 2002
Write clearly and explain everything you do, unless it is explicitely stated
that no explanation is needed.
Calculators are
not
allowed.
Don’t forget to
write your name on every page that you hand in. All problems are worth the
same.
1.
Are the following statements true or false? (no explanation needed, answer
with the full word “TRUE” or “FALSE” as some people’s “F” and “T” are very
similar)
a)
If
A
,
B
and
C
are ±nite sets and

A
∪
B

=

A
∪
C

, then

B

=

C

.
b)
If
A
and
B
are ±nite sets with

A

>

B

and
f
:
A
→
B
is a function, then
f
is onto.
c)
Let
f
and
g
be functions such that the composition
h
=
g
◦
f
exists ((
g
◦
f
)(
x
) =
g
(
f
(
x
))). If
h
is onetoone, then
g
is also onetoone.
d)
b
log
2
(6)
c
=

3.
e)
For all
x
and
y
we have
b
x
+
y
c ≤ b
x
c
+
b
y
c
.
f)
The proposition
p
↔
q
is equivalent with (
¬
p
∨
q
)
∧
(
p
∨ ¬
q
).
g)
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 Spring '08
 STRAIN
 Math, propositional functions

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