Use Tools of Set Algebra to Solve

1
Use Tools of Set Algebrato Solve

• Pamela Leutwyler

2
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches. How many men
are there? How many women are doctors? How many
lawyers drive Porsches?
3
tool box
To solve this problem, you might use the
following
Contrapositive Law If A?B then B ? ? A ?
De Morgans Law ( A ?B ) ? A ? ? B ?
A
B
z
x
y
xyz xy yz - y
n(A ?B)n(A)n(B) -n(A ?B)
The complement of the universe the empty set.
U ? ?
4
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
5
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
If D ?L U
D ?
L ?
then (D ?L) ? U? then D ? ? L ? ?
6
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
If L ? W
D ?
L ?
then W ? ? L ? and W ? M
M
7
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
If D ? P
D ?
L ?
P ?
then P ? ? D ?
M
8
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
3 do not drive Porsches.
D ?
L ?
P ?
M
3
9
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
n(U) n( D ?L) 30
D ?
L ?
n(D?L)n(D)n(L)-n(D?L)
P ?
M
30 21 17 - 8
3
10
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
n(U) n( D ?L) 30
D ?
L ?
n(D?L)n(D)n(L)-n(D?L)
P ?
M
30 21 17 - 8
3
8
11
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
D ?
L ?
P ?
M
3
6
8
12
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
D ?
L ?
P ?
M
3
6
4
8
13
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
D ?
L ?
P ?
M
3
9
6
4
8
14
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
D ?
L ?
P ?
M
3
9
6
4
8
15
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? How many women are
doctors? How many lawyers drive Porsches?
D ?
L ?
P ?
M
3
9
6
4
8
16
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? 9 How many women are
doctors? How many lawyers drive Porsches?
D ?
L ?
P ?
M
3
9
6
4
8
17
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? 9 How many women are
doctors? 12 How many lawyers drive Porsches?
D ?
L ?
P ?
M
3
9
4
6
8
18
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? 9 How many women are
doctors? 12 How many lawyers drive
Porsches? 14
D ?
L ?
P ?
M
3
9
6
4
8
19
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? 9 How many women are
doctors? 12 How many lawyers drive
Porsches? 14
D ?
L ?
P ?
M
3
9
6
4
8
20
a different approach
21
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
22
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
D
L
23
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
D
L
24
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
P
D
L
25
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
P
0
D
L
0
0
0
0
26
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
P
0
D
L
0
0
0
0
27
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
n(U) n( D ?L) 30
W
P
0
D
L
n(D?L)n(D)n(L)-n(D?L)
30 21 17 - 8
0
8
0
0
0
28
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
P
0
D
L
0
8
0
0
0
29
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
3 do not drive Porsches
W
P
0
D
L
3
0
8
0
0
0
30
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
P
0
D
L
3
6
0
8
0
0
0
31
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
P
0
D
L
3
6
0
8
4
0
0
0
32
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
W
P
0
D
L
3
6
0
8
4
9
0
0
0
33
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? 9 How many women are
doctors? 12 How many lawyers drive
Porsches? 14
W
P
0
D
L
3
6
0
8
4
9
0
0
0
34
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? 9 How many women are
doctors? 12 How many lawyers drive
Porsches? 14
W
P
0
D
L
3
6
0
8
4
9
0
0
0
35
30 friends meet at a college reunion. They are
all trying to impress one another. Every one of
them has a medical degree or a law degree and
some have both. All the lawyers are women. All
the doctors drive Porsches. There are 17
lawyers. There are 21 doctors. 27 drive
Porsches. 18 women drive Porsches.
How many men are there? 9 How many women are
doctors? 12 How many lawyers drive
Porsches? 14
W
P
0
D
L
3
6
0
8
4
9
0
0
0