Use Tools of Set Algebrato Solve

Pamela Leutwyler

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?

To solve this problem, you might use the following:

Contrapositive LawIf AB then B A

De Morgan’s Law

( A B ) = A B

n(A B)=n(A)+n(B) -n(A B)

A Bx y

z

x+y+z =x+y + y+z - y

U =

The complement of the universe = the empty set.

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.

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

then (D L) = U

then D L =

D L

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 If L W

then W L

and W = M

M

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 If D P

then P D

MP

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

MP

3 do not drive Porsches.

3

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

MP

3

n(U) = n( D L) = 30

n(DL)=n(D)+n(L)-n(DL)

30 = 21 + 17 - 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.

D L

MP

3

n(U) = n( D L) = 30

n(DL)=n(D)+n(L)-n(DL)

30 = 21 + 17 - 8

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.

D L

MP

3

8

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.

D L

MP

3

8

6 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.

D L

MP

3

8

6 4

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.

D L

MP

3

8

6 4

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.

D L

MP

3

8

6 4

9

How many men are there?How many women are doctors?How many lawyers drive Porsches?

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

MP

3

8

6 4

9

How many men are there? 9How many women are doctors?How many lawyers drive Porsches?

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

MP

3

8

6 4

9

How many men are there? 9How many women are doctors? 12How many lawyers drive Porsches?

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

MP

3

8

6 4

9

How many men are there? 9How many women are doctors? 12How many lawyers drive Porsches? 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

MP

3

8

6 4

9

How many men are there? 9How many women are doctors? 12How many lawyers drive Porsches? 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.

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

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 LW

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 LWP

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 LWP

0

0

0

0

0

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 LWP

0

0

0

0

0

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 LWP

0

0

0

0

0

n(U) = n( D L) = 30

n(DL)=n(D)+n(L)-n(DL)

30 = 21 + 17 - 88

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 LWP

0

0

0

0

0

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.

D LWP

0

0

0

0

0

8

3 do not drive Porsches

3

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 LWP

0

0

0

0

0

8 36

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 LWP

0

0

0

0

0

8 364

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 LWP

0

0

0

0

0

8 364

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.

D LWP

0

0

0

0

0

8 364

9

How many men are there? 9How many women are doctors? 12How many lawyers drive Porsches? 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 LWP

0

0

0

0

0

8 364

9

How many men are there? 9How many women are doctors? 12How many lawyers drive Porsches? 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 LWP

0

0

0

0

0

8 364

9

How many men are there? 9How many women are doctors? 12How many lawyers drive Porsches? 14