d)
“If everyone loves Larry then everyone loves Jerry.” :
2200
x L(x)
=>
2200
x J(x)
[last two were pretty tricky…]
Quiz 2:
(all questions viable for midterm!)
1)
Label each of the following
T
rue or
F
alse:
[18pts]
{1}
⊆
{1}
_T (case of A
⊆
A),
{1}
⊂
{1}
_F (not true because {1}={1}),
{1}
∈
{1} _
F
∅
∈
{1}
__F
,
∅
⊂
{1}
_T_(
∅
⊂
A for all non-empty sets A)
∅
∈
{
∅
}
_T__
2) [21pts]
If A = {s, t, t, q, r, t, q} and B = {t, v, t}, then.
(
First note that A={s,t,q,r} and B={t,v})
|A| = __
4
____,
|P(A)| = ___
2
4
=16
_______,
|A
×
B| = __
4*2=8
______
A
∩
B = ___
_{t}
A – B =
______{s,q,r}
A
∪
B = _____
{s,t,q,r,v}
{r,s,r}
×
B = ____
{r,s} x B = {(r,t),(r,v),(s,t),(s,v)}
3)
[12pts
] Compute the following values:
- 4.3
= __
-5
_____
4.3
= ___
5
_____
4/3
= __
1
_____
- 4/3
= ___
-1
_____
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.