MGF 1106 Exam lA

Name ~SWfr K~

ID ___________

HONOR CODE On my honor I have neither given nor received any aid on this examination

Signature _________________

Instructions Do all scratch work on the test itself Make sure your final answers are clearly labelled Be sure to simplify all answers whenever possible SHOW ALL WORK ON TIllS EXAM IN ORDER TO RECEIVE FULL CREDIT

No Score 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8

10 8 11 10 12 12

Bonus 10 I Total I 100 I

1 Express the following sets in set-builder notation using the most condensed notation possible

(a) April August 1t -ito

J(fl (b) 9 10 11 12

2 Express the following sets using the roster method

J ( ~I) (a) T he set of the four seasons in a year

Gfltlj funlII4I fJL Iltr J]

7 t~1- (b) x IXENand 6 ltxlt10

[1i ~I l IO )

cJf -C 3 Det ermine whether t he following sets are equal equivalent both or neit her Explain your answer

A = 12345

B = O 1234

a- d-(~lto 4 Calculate the number of subsets of the given set then list all the subsets

III III

cent

tr~ fIr) inrf l r 1L L fIl nrt fx nr I frlrJIrJ

5 Let

U = a b c d e j g h

A = ag h

B = bg h

C = bc d ej

Find each of the following sets

)fH (a) An B

[~I~) I

~ ~~5l) (b) B U C

C -= ~q ~I~)

[~JC = Q~5~D J~~$I (c) (A n C)

A() (-1gt_---- cent U ~ fC1b) c d t) f I ~ I ~ ~

)~dH~ (d) (A n B )u(A nC)

AI fbfCdlJf~ ~ An~~~~

AI ()C ~ cent 9gt Jb) U4 l~bli

4 ~l~ (e) (A U B ) n C

Ave fal ~~J ~ rAUB) I fcel euro +

kf a t- +Jnf~ IL ~Ie+~ =5c dItf f

6 Use t he Venn diagram to represent each set in roster form

J4 ~~ (a) A r--- --- _ y lJ ~3 4 $)( J 1~

z 41J3S (b) Au B

~ I ~ ~1 (c) (B U C)

4it ~~ (d) An B

[4 1 i I ~D

1~ it 4( (e) An B n C

Lhll

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

1 Express the following sets in set-builder notation using the most condensed notation possible

(a) April August 1t -ito

J(fl (b) 9 10 11 12

2 Express the following sets using the roster method

J ( ~I) (a) T he set of the four seasons in a year

Gfltlj funlII4I fJL Iltr J]

7 t~1- (b) x IXENand 6 ltxlt10

[1i ~I l IO )

cJf -C 3 Det ermine whether t he following sets are equal equivalent both or neit her Explain your answer

A = 12345

B = O 1234

a- d-(~lto 4 Calculate the number of subsets of the given set then list all the subsets

III III

cent

tr~ fIr) inrf l r 1L L fIl nrt fx nr I frlrJIrJ

5 Let

U = a b c d e j g h

A = ag h

B = bg h

C = bc d ej

Find each of the following sets

)fH (a) An B

[~I~) I

~ ~~5l) (b) B U C

C -= ~q ~I~)

[~JC = Q~5~D J~~$I (c) (A n C)

A() (-1gt_---- cent U ~ fC1b) c d t) f I ~ I ~ ~

)~dH~ (d) (A n B )u(A nC)

AI fbfCdlJf~ ~ An~~~~

AI ()C ~ cent 9gt Jb) U4 l~bli

4 ~l~ (e) (A U B ) n C

Ave fal ~~J ~ rAUB) I fcel euro +

kf a t- +Jnf~ IL ~Ie+~ =5c dItf f

6 Use t he Venn diagram to represent each set in roster form

J4 ~~ (a) A r--- --- _ y lJ ~3 4 $)( J 1~

z 41J3S (b) Au B

~ I ~ ~1 (c) (B U C)

4it ~~ (d) An B

[4 1 i I ~D

1~ it 4( (e) An B n C

Lhll

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

2 Express the following sets using the roster method

J ( ~I) (a) T he set of the four seasons in a year

Gfltlj funlII4I fJL Iltr J]

7 t~1- (b) x IXENand 6 ltxlt10

[1i ~I l IO )

cJf -C 3 Det ermine whether t he following sets are equal equivalent both or neit her Explain your answer

A = 12345

B = O 1234

a- d-(~lto 4 Calculate the number of subsets of the given set then list all the subsets

III III

cent

tr~ fIr) inrf l r 1L L fIl nrt fx nr I frlrJIrJ

5 Let

U = a b c d e j g h

A = ag h

B = bg h

C = bc d ej

Find each of the following sets

)fH (a) An B

[~I~) I

~ ~~5l) (b) B U C

C -= ~q ~I~)

[~JC = Q~5~D J~~$I (c) (A n C)

A() (-1gt_---- cent U ~ fC1b) c d t) f I ~ I ~ ~

)~dH~ (d) (A n B )u(A nC)

AI fbfCdlJf~ ~ An~~~~

AI ()C ~ cent 9gt Jb) U4 l~bli

4 ~l~ (e) (A U B ) n C

Ave fal ~~J ~ rAUB) I fcel euro +

kf a t- +Jnf~ IL ~Ie+~ =5c dItf f

6 Use t he Venn diagram to represent each set in roster form

J4 ~~ (a) A r--- --- _ y lJ ~3 4 $)( J 1~

z 41J3S (b) Au B

~ I ~ ~1 (c) (B U C)

4it ~~ (d) An B

[4 1 i I ~D

1~ it 4( (e) An B n C

Lhll

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

cJf -C 3 Det ermine whether t he following sets are equal equivalent both or neit her Explain your answer

A = 12345

B = O 1234

a- d-(~lto 4 Calculate the number of subsets of the given set then list all the subsets

III III

cent

tr~ fIr) inrf l r 1L L fIl nrt fx nr I frlrJIrJ

5 Let

U = a b c d e j g h

A = ag h

B = bg h

C = bc d ej

Find each of the following sets

)fH (a) An B

[~I~) I

~ ~~5l) (b) B U C

C -= ~q ~I~)

[~JC = Q~5~D J~~$I (c) (A n C)

A() (-1gt_---- cent U ~ fC1b) c d t) f I ~ I ~ ~

)~dH~ (d) (A n B )u(A nC)

AI fbfCdlJf~ ~ An~~~~

AI ()C ~ cent 9gt Jb) U4 l~bli

4 ~l~ (e) (A U B ) n C

Ave fal ~~J ~ rAUB) I fcel euro +

kf a t- +Jnf~ IL ~Ie+~ =5c dItf f

6 Use t he Venn diagram to represent each set in roster form

J4 ~~ (a) A r--- --- _ y lJ ~3 4 $)( J 1~

z 41J3S (b) Au B

~ I ~ ~1 (c) (B U C)

4it ~~ (d) An B

[4 1 i I ~D

1~ it 4( (e) An B n C

Lhll

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

a- d-(~lto 4 Calculate the number of subsets of the given set then list all the subsets

III III

cent

tr~ fIr) inrf l r 1L L fIl nrt fx nr I frlrJIrJ

5 Let

U = a b c d e j g h

A = ag h

B = bg h

C = bc d ej

Find each of the following sets

)fH (a) An B

[~I~) I

~ ~~5l) (b) B U C

C -= ~q ~I~)

[~JC = Q~5~D J~~$I (c) (A n C)

A() (-1gt_---- cent U ~ fC1b) c d t) f I ~ I ~ ~

)~dH~ (d) (A n B )u(A nC)

AI fbfCdlJf~ ~ An~~~~

AI ()C ~ cent 9gt Jb) U4 l~bli

4 ~l~ (e) (A U B ) n C

Ave fal ~~J ~ rAUB) I fcel euro +

kf a t- +Jnf~ IL ~Ie+~ =5c dItf f

6 Use t he Venn diagram to represent each set in roster form

J4 ~~ (a) A r--- --- _ y lJ ~3 4 $)( J 1~

z 41J3S (b) Au B

~ I ~ ~1 (c) (B U C)

4it ~~ (d) An B

[4 1 i I ~D

1~ it 4( (e) An B n C

Lhll

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

5 Let

U = a b c d e j g h

A = ag h

B = bg h

C = bc d ej

Find each of the following sets

)fH (a) An B

[~I~) I

~ ~~5l) (b) B U C

C -= ~q ~I~)

[~JC = Q~5~D J~~$I (c) (A n C)

A() (-1gt_---- cent U ~ fC1b) c d t) f I ~ I ~ ~

)~dH~ (d) (A n B )u(A nC)

AI fbfCdlJf~ ~ An~~~~

AI ()C ~ cent 9gt Jb) U4 l~bli

4 ~l~ (e) (A U B ) n C

Ave fal ~~J ~ rAUB) I fcel euro +

kf a t- +Jnf~ IL ~Ie+~ =5c dItf f

6 Use t he Venn diagram to represent each set in roster form

J4 ~~ (a) A r--- --- _ y lJ ~3 4 $)( J 1~

z 41J3S (b) Au B

~ I ~ ~1 (c) (B U C)

4it ~~ (d) An B

[4 1 i I ~D

1~ it 4( (e) An B n C

Lhll

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

6 Use t he Venn diagram to represent each set in roster form

J4 ~~ (a) A r--- --- _ y lJ ~3 4 $)( J 1~

z 41J3S (b) Au B

~ I ~ ~1 (c) (B U C)

4it ~~ (d) An B

[4 1 i I ~D

1~ it 4( (e) An B n C

Lhll

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

14rt 4Co 7 Construct a Venn diagram illustrating the given sets

u

A = aehi

B = b c e j h i C = e jg

U = a b c d e j g h i

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

8 Express the quantified statement in an equivalent way t hen write the negation of the quantified statement

31-ifdi (a) All whales are mammals

erVi~ lWe we Vlo ~ It s iW- W( IIOf- ~~s

~~poundUl~ ~ Sc~ ~s art flof ~~~~

~ (( 0 (b) Some students are business majors

viVJw- T4r( VJcis-ls td l~s+ thJ s~ wlo is ~ ovsraquotss ~~

~4~ tvo s~ off biMSS ~0tS

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

9 Let p q and r be the given simple statements Write each compound statement in symbolic form

~ 113 (a) p Im leaving q Youre staying

Youre staying and Im not leaving

~ d-tJ (b) p You are human q You have feathers

Not being human is necessary for not having feathers

~ dI-t(oD (c) p The temperature outside is freezing q The heater is working r The house is cold

If t he temperature outside is freezing then the heater is working or the house is not cold

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

10 Let p q and r be the given simple statements Write each symbolic statement in words

1 ~rt~)(a) p The heater is working q The house is warm

3 ~ i~5~ (b) p Romeo loves Juliet q Juliet loves Romeo

+

CJ (q V p)

~ J I--~1(c) p The temperature is above 85deg q We finished studying r We go to the beach

(p V q) -gt r

Ie ~ ~~ i S ~ lbS) CN Wt ~Y6ltJ s+VJ I +k

~ ~ -n ~ ~c1

11 Determine whet her each statement is t rue or false

Jl-J-d=gt (a) Ralph E Ralph Alice Trixie Norton

TnJe

(b) Canada C Mexico United States Canada

(c) Ralph C Ralph Alice Trixie Norton

True

(d) 4 E 48

TrJt

(e) I 4 ~ 4 I

FtJs~

1s 4~ 12 A survey of 180 college students was t aken to determine particshyipation in various campus activities Forty-three students were in fraternit ies 52 participated in campus sports and 35 particshyipated in various campus tutorial programs Thirteen students participated in fraternities and sports 14 in sports and tutorial programs and 12 in fraternities and tutorial programs Five students participated in all three activit ies Of those surveyed

(a) How many part icipated in only campus sports

(b) How many participated in fraternities and sports but not tutorial programs

(c) How many participated in fraternities or sports but not tutorial programs

(01

(d) How many participated in exactly one of these activities

(e) How many participated in at least two of t hese activities

(f) How many did not participate in any of t he three activities

Bonus Prove that the following sets are equal Give as much exshyplanation as possible

((A n B) U C) = (A n C) U (B n C)

((Ane)uc) (1115) n c ~ 11 MIJr~ s ~gtJs

(A UB) (1 t L ~ ~j~IS ~s

- (A (c) U(B1nC) ~7 +eurot Pi6tribUPW LAw

DR

u

C It)

~1i~V ( - I 1 ~~

l(Mro)VC Y=~ ~11-

A ~ gt (11)~

AI nc=( t

s -= f 4 11~

BlnC 411shy

(A()(VCBnc) LlCl

n ~o ~ art ~lU1-kJ ~ ~ SCt~ nJj I)t~ So itt AA QJe wJ

1s 4~ 12 A survey of 180 college students was t aken to determine particshyipation in various campus activities Forty-three students were in fraternit ies 52 participated in campus sports and 35 particshyipated in various campus tutorial programs Thirteen students participated in fraternities and sports 14 in sports and tutorial programs and 12 in fraternities and tutorial programs Five students participated in all three activit ies Of those surveyed

(a) How many part icipated in only campus sports

(b) How many participated in fraternities and sports but not tutorial programs

(c) How many participated in fraternities or sports but not tutorial programs

(01

(d) How many participated in exactly one of these activities

(e) How many participated in at least two of t hese activities

(f) How many did not participate in any of t he three activities

Bonus Prove that the following sets are equal Give as much exshyplanation as possible

((A n B) U C) = (A n C) U (B n C)

((Ane)uc) (1115) n c ~ 11 MIJr~ s ~gtJs

(A UB) (1 t L ~ ~j~IS ~s

- (A (c) U(B1nC) ~7 +eurot Pi6tribUPW LAw

DR

u

C It)

~1i~V ( - I 1 ~~

l(Mro)VC Y=~ ~11-

A ~ gt (11)~

AI nc=( t

s -= f 4 11~

BlnC 411shy

(A()(VCBnc) LlCl

n ~o ~ art ~lU1-kJ ~ ~ SCt~ nJj I)t~ So itt AA QJe wJ

Bonus Prove that the following sets are equal Give as much exshyplanation as possible

((A n B) U C) = (A n C) U (B n C)

((Ane)uc) (1115) n c ~ 11 MIJr~ s ~gtJs

(A UB) (1 t L ~ ~j~IS ~s

- (A (c) U(B1nC) ~7 +eurot Pi6tribUPW LAw

DR

u

C It)

~1i~V ( - I 1 ~~

l(Mro)VC Y=~ ~11-

A ~ gt (11)~

AI nc=( t

s -= f 4 11~

BlnC 411shy

(A()(VCBnc) LlCl

n ~o ~ art ~lU1-kJ ~ ~ SCt~ nJj I)t~ So itt AA QJe wJ