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Sec. 2.2 Subsets Liberal Arts Math

def Set A is a subset of set B, denoted A

B , if and only if all the elements of set A

are also elements of set B

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a subset of set B, denoted A

B , if and only if all the elements of set A

are also elements of set B

ex. 1 Determine whether set A is a subset of

set B. a) A b, d, g

B a, b, c, d, e, f, g b) A 1, 2,

3, 4, 5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a subset of set B, denoted A

B , if and only if all the elements of set A

are also elements of set B

ex. 1 Determine whether set A is a subset of

set B. a) A b, d, g

B a, b, c, d, e, f, g b) A 1, 2,

3, 4, 5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

A B

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a subset of set B, denoted A

B , if and only if all the elements of set A

are also elements of set B

ex. 1 Determine whether set A is a subset of

set B. a) A b, d, g

B a, b, c, d, e, f, g b) A 1, 2,

3, 4, 5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

A B

A B

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a subset of set B, denoted A

B , if and only if all the elements of set A

are also elements of set B

ex. 1 Determine whether set A is a subset of

set B. a) A b, d, g

B a, b, c, d, e, f, g b) A 1, 2,

3, 4, 5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

A B

A B

A B

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a proper subset of set B,

denoted A B, iff (if and only if) all

the elements of set A are elements of set B

and set A set B

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a proper subset of set B,

denoted A B, iff (if and only if) all

the elements of set A are elements of set B

and set A set B (ie., set B

must contain at least one element not in set A).

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a proper subset of set B,

denoted A B, iff (if and only if) all

the elements of set A are elements of set B

and set A set B (ie., set B

must contain at least one element not in set A).

ex. 2 Determine whether set A is a proper

subset of set B. a) A b, d, g B a,

b, c, d, e, f, g b) A 1, 2, 3, 4,

5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a proper subset of set B,

denoted A B, iff (if and only if) all

the elements of set A are elements of set B

and set A set B (ie., set B

must contain at least one element not in set A).

ex. 2 Determine whether set A is a proper

subset of set B. a) A b, d, g B a,

b, c, d, e, f, g b) A 1, 2, 3, 4,

5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

A B

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a proper subset of set B,

denoted A B, iff (if and only if) all

the elements of set A are elements of set B

and set A set B (ie., set B

must contain at least one element not in set A).

ex. 2 Determine whether set A is a proper

subset of set B. a) A b, d, g B a,

b, c, d, e, f, g b) A 1, 2, 3, 4,

5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

A B

A B

Sec. 2.2 Subsets Liberal Arts Math

def Set A is a proper subset of set B,

denoted A B, iff (if and only if) all

the elements of set A are elements of set B

and set A set B (ie., set B

must contain at least one element not in set A).

ex. 2 Determine whether set A is a proper

subset of set B. a) A b, d, g B a,

b, c, d, e, f, g b) A 1, 2, 3, 4,

5, 6 B 2, 4, 6 c) A

?,?,? B ?, ?, ?

A B

A B

A B

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

True

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

True

False

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

True

False

True

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

True

False

True

False

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

True

False

True

True

False

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

True

False

True

True

True

False

Sec. 2.2 Subsets Liberal Arts Math

- ex. 3 Determine whether the following are True

or False - 3 1, 2, 3
- 3 1, 2, 3 e) 3 1, 2, 3
- 3 f) 3 1, 2, 3
- d) 3 1, 2, 3 g) 1, 2, 3

True

False

True

True

True

False

True

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 1, 2, 3, 4 1,

2, 3, 4, 5

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3,

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

32

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

32

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

1, 2, 3, 4, 5, , 10

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

32

, 1, 2, 1, 2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

1, 2, 3, 4, 5, , 10

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

32

, 1, 2, 1, 2

2x2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

1, 2, 3, 4, 5, , 10

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

32

, 1, 2, 1, 2

2x2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

2x2 x 2

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

1, 2, 3, 4, 5, , 10

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

32

, 1, 2, 1, 2

2x2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

2x2 x 2

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

2x2x2 x 2

1, 2, 3, 4, 5, , 10

Sec. 2.2 Subsets Liberal Arts Math

Number

of set distinct subsets Note

1 2 , 1 1, 2

4 1, 2, 3 8 1,

2, 3, 4 16 1, 2, 3, 4, 5

32

, 1, 2, 1, 2

2x2

, 1, 2, 3, 1, 2, 1, 3, 2, 3,

1, 2, 3

2x2 x 2

, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4,

2, 3, 2, 4, 3, 4, 1, 2, 3, 1, 2, 4 ,

1,3,4, 2, 3, 4, 1, 2, 3, 4

2x2x2 x 2

1, 2, 3, 4, 5, , 10

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