2–Exercises 1–Deﬁnitions Setsandrelations

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Season 1 • Episode AP06 • Sets and relations

⁰

Sets and relations

Season 1

Episode AP06 Time frame 55 mins

Objectives :

•

Întrodue ^the ônept ôf ^sets ând ^relations.

•

Întrodue ^the ^main ôperationsôn ^sets ^: ûnion,intersetion and omplement.

•

^Introdue ^the ^symbols

∈

^,

6∈

^,

⊂

^,

6⊂

^,

∪

^,

∩

^.

•

^Use ^of ^Venn ^diagram

Materials :

•

¹ ôpy ^per^student ôf ^the êxerise ^sheet.

•

^Slideshow.

1 – Definitions 10 mins

Using aslideshow, the teaher introdue the main onepts.

2 – Exercises remaining time

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Sets and relations

Season 1

Episode AP06 Document 55 mins

Sets and memberships

1. Let

Ω

^be ^an ^universe,

A

^and

B

^two ^subsets ^of

Ω

^. ^Desribe

A

^,

A ∩ B

^and

A ∪ B

when :

(a)

Ω = {1; 2; 3; 4; 5; 6}; A = {1; 5; 6}

^and

B = {2; 5}

^.

(b)

Ω

^={blue^;white^;red^;yellow}^;

A =

^{blue^;yellow} ^and

B =

^{red}.

()

Ω = {a; b; c; d; e; f ; g}; A = {a; b; f ; g; e}

^and

B = {b; c; d}

^.

2. Let

A = {b; r; a; v; o}

^and

B = {t; r; i; o}

^.

Fillout the blanks with the symbols

=, ∈, 6∈, ⊂, 6⊂

^:

(a)

a . . . A

(b)

{t; r; a} . . . B

()

r . . . A ∩ B

(d)

{r; i} . . . A ∩ B

(e)

{r; i} . . . A ∩ B

(f)

{s} . . . A ∪ B

(g)

{ b; r; a; v ; o } . . . A ∪ B

(h)

i . . . A ∩ B

(i)

{b; a; t; i; v; o; r} . . . A ∪ B

3. Wepik out randomlya ard ina 52playing ards dek. Consider the events :

• A

^: ^Piking ^an^ae^;

• K

^: ^Piking ^an^king^;

• D

^: ^Piking ^an^diamond^;

• B

^: ^Piking^an ^blak ^ard^;

• F

^: ^Piking ^an ^gure ^(jak, ^queen

orking);

Givethe probabilityof the events :

(a)

A

^;

(b)

K

^;

()

D

^;

(d)

B

^;

(e)

F

^;

(f)

A ∩ D

^;

(g)

A ∩ B

^;

(h)

B ∩ F

^;

(i)

A ∪ D

^;

(j)

A ∪ B

^;

(k)

B ∪ F

^;

(l)

A ∪ F

^;

(m)

A ∩ F

^;

(n)

A ∩ K ∩ F

^;

(o)

A ∪ K ∪ F

^;

(p)

A ∩ K

^;

(q)

A ∪ K

^;

Venn diagram

1. Let

Ω

^be^an^universe,

A

^and

B

^two ^subsets^of

Ω

^.^Illustrate^with ^Venn^diagrams^the

followingsituations :

(a)

Ω = { 1; 2; 3; 4; 5; 6 } ; A = { 1; 5; 6 }

^and

B = { 2; 5 }

^.

(b)

Ω

^={blue^;white^;red^;yellow}^;

A =

^{blue^;yellow} ^and

B =

^{red}.

()

Ω = {a; b; c; d; e; f ; g}; A = {a; b; f ; g; e}

^and

B = {b; c; d}

^.

2. in a lass with 25 students, 15play musi, 8 play hess and 3 play both musi and

hess.

(a) Draw the Venn diagramrelated tothe situation.