Chapter 1 Answers

CHAPTER 1 - ANSWERS

EXERCISES 1A

1.	Descriptions a, d, and f are precise enough, but the others are probably not.

2.	a.	{HST , DDE , JFK , LBJ , RMN , GRF , JEC , RWR , GHWB , WJC , GWB}
2.	b.	{x : x is a sequence of initials of a U.S. president in the second half of the twentieth century}

3.

a.

{red , blue , yellow}

b.

{y : y is a primary color}

4.	a.	{1 , 3 , 5 , 7 , 9}
	b.	{3 , 6 , 9 , 12 , 15 , …}
	c.	{Hawaii , Kauai , Lanai , Maui , Molokai , Oahu}
	d.	{a , b , c , d , e , f , g}
	e.	{m , n}

5.	a.	{x : x is a positive integer less than 10}
	b.	{y : y is an odd positive integer}
	c.	{# : # is a consonant in the English alphabet}
	d.	{z : z is a state of the U.S. not bordering another state}
	e.	{f : f is the first name of a U.S. first lady in the second half of the twentieth century}

6.	You should find 16 subsets. A set with 5 elements has 32 subsets.

7.	a.	false	b.	true	c.	false	d.	true	e.	false
	f.	true	g.	false	h.	true	i.	false	j.	false
	k.	false	l.	false	m.	true	n.	false	o.	true

8.	a.	C and D, C and F, D and E
	b.	D Ì A, E Ì B, F Ì A
	c.	A, B, F
	d.	~A = {w , x} , ~B = {u , x} , ~C = {u , v , z}
	e.	C, E

9.	a.	P Ì F	b.	F Ì L	c.	F Ì ~L	d.	S Ë W	e.	P Ë ~B
	f.	B Ì ~S	g.	~F Ì W	h.	~B Ë S	i.	L Ë B	j.	~L Ë ~P

10.	a.	December days are cold.
	b.	Not all December days are cold.
	c.	Rainy days are not nice.
	d.	Some June days are rainy.
	e.	Not all June days are warm.
	f.	No nice days occur in December.
	g.	Days not nice are cold.
	h.	Some days not nice are warm.
	i.	Some warm days occur in December.
	j.	Not every nonrainy day occurs in June.

EXERCISES 1B

1.	a.	{b,d,e}	b.	{c,g}	c.	{a,b,c,d,g}	d.	{a,d}
	e.	{e}	f.	{b,c,d,e,g}	g.	{c}	h.	{a,b,c,d,f,g}
	i.	{a,b,c}	j.	{a,b,c,f,g}	k.	{a,c,d,e,f}	l.	{a,c,d,e}

2.	A ∩ B = A , A È B = B , A ∩ ~B = Æ

3.	a. brown female cows		b. cows that are Jersey or contented
	c. contented male cows		d. cows that are energetic, or white, or have horns
	e. brown discontented Jersey cows		f. horned cows that are lazy or discontented
	g. Guernseys without horns		h. cows that are female, or a contented Guernsey

	i. B ∩ J		j. B È F		k. C ∩ ~J		l. ~F ∩ (J È ~B)
	m. ~C ∩ ~H		n. L È (B ∩ H)		o. L ∩ ~C ∩ ~F		p. ~B È J È H

	q. The female Jersey cows are contented.
	r. Some Jersey cows with horns are discontented.
	s. The brown lazy cows are contented Guernseys.
	t. The Guernsey cows are brown and energetic.
	u. Not all lazy discontented cows are males with horns.
	v. Cows energetic or contented have no horns.
	w. There are no female discontented cows.
	x. No cow with horns is lazy or discontented.
	y. Every cow is contented and energetic.

	z. L Ì (C ∩ J)		@. (~F ∩ H ∩ ~J) Ì ~L		#. (F ∩ B) Ì (C ∩ ~H ∩ J)
	$. (L ∩ B) Ë (F ∩ J)		%. (F ∩ H) Ì (~B ∩ L)		&. C ∩ B ∩ ~F = Æ
	*. B ∩ H ∩ L ∩ ~C = Æ		!. U = (~L ∩ F) È (L ∩ ~F)		+. (L È ~C) Ë (~H ∩ ~F ∩ ~J)

4.	a. tasty red tomatoes		b. tomatoes that are red or tasty or juicy
	c. green imported tomatoes		d. tomatoes that are hard, or green and bland
	e. tomatoes juicy or tasty		f. tomatoes not either plump or juicy
	g. plump local soft tomatoes		h. imported tomatoes that are not plump or hard

	i. L ∩ J		j. ~T È ~J		k. ~H ∩ J ∩ P
	l. H ∩ (~R È ~J)		m. (P È J) ∩ ~L		n. ~T È (H ∩ ~R)

	o. Local red tomatoes are juicy.
	p. Hard tomatoes are bland and dry.
	q. There are no hard imported juicy tomatoes.
	r. Some juicy plump tomatoes are bland.
	s. Tomatoes that are hard or bland are dry.
	t. Red plump tomatoes are juicy and tasty.

	u. R Ë L		v. T ∩ ~L = Æ		w. (~R ∩ J) Ì ~T
	x. (P ∩ J ∩ L) Ì (R ∩ T)		y. (~L ∩ P) Ì (~J ∩ ~T)		z. (P È J) Ë (~H ∩ T)

EXERCISES 1C

1.

a.

Venn Diagram

b.

Venn Diagram

2.	Shade the two sides of the equation in different Venn diagrams, and check that the two shadings are the same.

3.	Shade the two sides of the equation in different Venn diagrams, and check that the two shadings are the same.

4.	a.			b.
	c.			d.

5.	a.			b.			c.
	d.			e.			f.

EXERCISES 1D

1.

a.

37

b.

5

c.

17

2.

a.

8

b.

39

c.

46

d.

28

e.

43

f.

22

3.	13 (What rule involving sets did you use?)

4.

a.

19

b.

1

c.

3

d.

7

5.

a.

7

b.

23

c.

11

d.

24

e.

59

6.	a.	8	b.	6	c.	4	d.	11	e.	21
6.	f.	14	g.	18	h.	28	i.	7	j.	10

7.	a.	5	b.	12	c.	17	d.	22
7.	e.	9	f.	19	g.	16