MATH 110 Test 2 Extra In-Class Review Problems Find n(A) if A = { 200, 201, 202, 203, …, 255 }

MATH 110 Test 2 Extra In-Class Review Problems

Find n(A) if A = { 200 , 201, 202, 203 , … , 255 }


Find n(A) if A = { 200 , 201, 202, 203 , … , 255 }

255 – 200 + 1 = 56


A B C D E F G

The graph to the right shows the number of hits (in millions) for 7 web pages. Use the listing method to list the set of web pages that have a number of visitors less than 40 million.


A B C D E F G

The graph to the right shows the number of hits (in millions) for 7 web pages. Use the listing method to list the set of web pages that have a number of visitors less than 40 million.

{ A , B , C , E , G }

True or FalseThe sets and { } are equal.

MATH 110 Sec 2-2: Comparing SetsPractice Exercises

True or FalseThe sets and { } are equal.


is the empty set. That means that it does not have ANY elements. is also the empty set. is no longer empty.

An empty set, , can’t be equal a set that is not empty, .

The sets are NOT equal and the statement above is FALSE.

True or FalseThe sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equal.


True or FalseThe sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equal.


It is easy to see here that these two sets do not have exactly the same elements.

Remember that two sets are equal if and only if they have exactly the same elements.

The sets are NOT equal and the statement above is FALSE.

MATH 110 Sec 2-2: Comparing SetsPractice Exercises True or False

{ 12 , 82 , 99 } and { a , e, p } are equivalent.


{ 12 , 82 , 99 } and { a , e, p } are equivalent.

Remember that two sets are equivalent if they have the same number of elements.

321321

There are 3 elements in each set so the two sets are equivalent.

The statement above is TRUE.


The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equivalent.


The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o , u} are equivalent.


321 4 5 321 4 5

There are 5 elements in each set so the two sets are equivalent.

The statement above is TRUE.


The sets {1, 2 , 3 , 4 , 5} and {a , e , i , o} are equivalent.




321 4 5 321 4

There are 5 elements in one set and 4 in the other setso the two sets are NOT equivalent.




321 4 5 321 4

There are 5 elements in one set and 4 in the other setso the two sets are NOT equivalent.

The statement above is FALSE.


Given the set A = {1, 3 , 7 , 9 , 15, 16}

How many subsets does A have?

How many proper subsets does A have?


How many subsets does A have?

How many proper subsets does A have?

26=64

Given the set A = {1, 3 , 7 , 9 , 15, 16}

26−1=63

A pizza place offers mushrooms, tomatoes and sausage as toppings for a plain cheese base. How many different types of pizzas can be made?


A pizza place offers mushrooms, tomatoes and sausage as toppings for a plain cheese base. How many different types of pizzas can be made?


The set of possible toppings is { M , T , S }

Every subset of this set is a different pizza.So, there are

different types of pizzas possible.

Remember: A set with k elements has subsets.

(A U C) ∩ B =

A U C =

U = { a , b , c , d , e , f , g , h , i , j , k }A = { a , b , f , h , i , j } B = { a , c , d , h , j } C = { a , d , f , g , j }

MATH 110 Sec 2-3: Set OperationsPractice Exercises

A ∩ C =Find:

(A U C) ∩ B = { a , b , d , f , g , h , i , j } ∩ { a , c , d , h , j }

U = { a , b , c , d , e , f , g , h , i , j , k }A = { a , b , f , h , i , j } B = { a , c , d , h , j } C = { a , d , f , g , j }

A U C = { a , b , d , f , g , h , i , j }

The intersectionof sets A and C, denoted A ∩ C:

The set of elements thatare in BOTH A and C.


A ∩ C = { a , f , j }Find:

The unionof sets A and C, denoted A C:

The set of elements thatare in EITHER A or C (or both).

(A U C) ∩ B = { a , d , h, j }

U = { hammer , moon , radio , muffin , cookie , chair , apple , fish , bread , grape }M = { x : x is human-made } E = { y : y is edible }


M ∩ E' =Find:

U = { hammer , moon , radio , muffin , cookie , chair , apple , fish , bread , grape }M = { x : x is human-made } E = { y : y is edible }


M ∩ E' = { hammer , radio , chair }Find: The intersection

of sets A and C, denoted A ∩ C:The set of elements that

are in BOTH A and C.

Putting this into words, we want human-made items that are NOT edible.

NOT

U = { hammer , moon , radio , muffin , cookie , chair , apple , fish , bread , grape }

man-made

man-made

man-made

man-made

man-made

man-made

NOT edible

NOT edible

NOT edible

NOT edible

U = { a , b , c , d , e , f , g , h }


Car Cost Size Warranty Safety Antitheft

a $22800 midrange 4 yrs poor YESb $23900 midrange 4 yrs good NOc $17300 subcompact 4 yrs good YESd $21800 compact 4 yrs poor NOe $18300 subcompact 2 yrs good NOf $19800 subcompact 4 yrs poor NOg $20900 compact 2 yrs poor YESh $20200 compact 4 yrs poor NO

W means“warranty is at least 3yrs”

G means “has good safety record”

W ∩ G‘ =

W means“warranty is at least 3yrs”

G means “has good safety record”

G‘ means “does not have a good safety record”

W ∩ G‘ = {a , d , f , h}

U = { a , b , c , d , e , f , g , h }


Car Cost Size Warranty Safety Antitheft

a $22800 midrange 4 yrs poor YESb $23900 midrange 4 yrs good NOc $17300 subcompact 4 yrs good YESd $21800 compact 4 yrs poor NOe $18300 subcompact 2 yrs good NOf $19800 subcompact 4 yrs poor NOg $20900 compact 2 yrs poor YESh $20200 compact 4 yrs poor NO

So, only a , d , f and h have warranties of at least 3 years and do not have good safety records.

If A ∩ B=Ø, then A and B are:a. complementsb. disjointc. emptyd. inclusive


If A ∩ B=Ø, then A and B are:a. complementsb. disjointc. emptyd. inclusive


A survey of 260 families:

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

99 had a dog 98 had neither a dog nor a cat76 had a cat and also had no parakeet34 had a dog & cat 8 had a dog, a cat & a parakeet

U

A

C

BHow many had a parakeet only?

A survey of 260 families:


99 had a dog 98 had neither a dog nor a cat76 had a cat and also had no parakeet34 had a dog & cat 8 had a dog, a cat & a parakeet

U

A

C

BHow many had a parakeet only?

21


The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, findn(G (A D). Mammals

(A)Birds(B)

Reptiles(C)

Fish(D)

Total

Morning(E) 111 54 6 80 251

Afternoon(F) 31 9 1 29 70

Evening(G) 10 3 48 24 85

Total 152 66 55 133 406


The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, findn(G (A D). Mammals

(A)Birds(B)

Reptiles(C)

Fish(D)

Total

Morning(E) 111 54 6 80 251

Afternoon(F) 31 9 1 29 70

Evening(G) 10 3 48 24 85

Total 152 66 55 133 406

Answer:n(G (A D) = 34

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MATH 110 Test 2 Extra In-Class Review Problems Find n(A) if A = { 200, 201, 202, 203, …, 255 }