d)
“If everyone loves Larry then everyone loves Jerry.” :
__________________
ICS.6D: Discrete Mathematics For Computer Science, Fall 2007, Quiz 2
1)
Label each of the following
T
rue or
F
alse:
{1}
⊆
{1} ____,
{1}
⊂
{1} ____,
{1}
∈
{1} ____,
[21pts]
∅
∈
{1} ___,
∅
⊂
{1} ____,
∅
∈
{1} ____,
∅
∈
{
∅
}
____
2) [21pts]
If A = {s, t, t, q, r, t, q} and B = {t, v, t}, then
|A| = ______,
|P(A)| = __________,
|A
×
B| = ________
A
∩
B = _________________________
A – B = ______________________________
A
∪
B = _________________________________________,
{r,s,r}
×
B = ______________________________________
3)
[12pts
] Compute the following values:
- 4.3
= _______
4.3
= ________
4/3
= _______
- 4/3
= ________
4) [20pts]
State whether each of these functions from
Z
to
Z
(
Z
=Integers
) is
I
njective (one-to-
one
),
S
urjective (onto
),
B
ijective, or
N
either, and
briefly
explain/justify each answer.
f(n) = 5n+1
___________________________________________________________
f(n) = n
2
- 4
___________________________________________________________
f(n) =
n / 5
___________________________________________________________
f(n) = 5 - n
____________________________________________________________
5) [26pts]
Prove the following claim (for any sets A and B):
A
∩
(B - A)
⊆
∅
Do it on the next page
where we list several facts that can be useful in this claim.
You don’t
have to
use all the facts listed or explain which of the stated facts you are using.
We’ll give partial credit if some part of your argument is correct and other part is not.