there are 3 questions and i need details of every step. 1
61  Midterm 1 Practice
Question 1
Let
F
(1)
=
F
(2)
=
1, and
F
(
n
)
=
F
(
n

1)
+
F
(
n

2),
n
?
3 be the Fibonacci numbers. Prove that
F
(3
k
)
is even for
k
=
1
,
2
,
3
, . . .
.
.........
Question 2
Let
X
=
{
1
,
2
,
3
} × {
3
,
6
}
be a set, with a relation
±
de?ned as (
a
,
b
)
±
(
c
,
d
) i
?
a
+
b
?
c
+
d
. Prove that
±
is a partial ordering and draw a Hasse diagram for the poset (
X
,
±
).
.........
Question 3
For two sets
A
,
B
, prove that
P
(
A
)
? P
(
B
)
? P
(
A
?
B
).
.........
P
uck
R
ombach
D
iscrete
S
tructures
M
idterm
1
Answer