Deck 2: Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Question 1

Prove that by giving a containment proof (that is, prove that the left side is a subset of the right side and that the right side is a subset of the left side).

Answer 1

Let and and and Reversing the steps gives the opposite containment.

Question 2

For each of the pairs of sets in 1-3 determine whether the first is a subset of the second, the second is a subset
of the first, or neither is a subset of the other.
The set of animals living in the ocean, the set of fish.

Answer 2

Neither is a subset of the other.

Question 3

Prove that by giving a Venn diagram proof.

Answer 3

Question 4

use a Venn diagram to determine which relationship, is true for the pair of sets.

Question 5

Prove that by giving a proof using logical equivalence.

Question 6

Prove or disprove:

Question 7

Prove that by giving an element table proof.

Question 8

Prove or disprove: if A, B , and C are sets, then

Question 9

use a Venn diagram to determine which relationship, is true for the pair of sets.

Question 10

use a Venn diagram to determine which relationship, is true for the pair of sets.

Question 11

Prove that by giving a Venn diagram proof.

Question 12

use a Venn diagram to determine which relationship, is true for the pair of sets.

Question 13

Prove that by giving an element table proof.

Question 14

Prove that by giving a containment proof (that is, prove that the left side is a subset of the right side and that the right side is a subset of the left side).

Question 15

determine whether the given set is the power set of some set. If the set is a power set, give
the set of which it is a power set.

Question 16

Prove or disprove

Question 17

determine whether the given set is the power set of some set. If the set is a power set, give
the set of which it is a power set.

Question 18

Prove that by giving a proof using logical equivalence.

Question 19

For each of the pairs of sets in 1-3 determine whether the first is a subset of the second, the second is a subset
of the first, or neither is a subset of the other.
The set of students studying a programming language, the set of students studying Java.

Question 20

For each of the pairs of sets in 1-3 determine whether the first is a subset of the second, the second is a subset
of the first, or neither is a subset of the other.
The set of people who were born in the U.S., the set of people who are U.S. citizens.

Question 21

determine whether the given set is the power set of some set. If the set is a power set, give
the set of which it is a power set.

Question 22

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 23

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 24

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 25

determine whether the given set is the power set of some set. If the set is a power set, give
the set of which it is a power set.

Question 26

determine whether the given set is the power set of some set. If the set is a power set, give
the set of which it is a power set.
Prove that

Question 27

Find

Question 28

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 29

Find

Question 30

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 31

Find

Question 32

Find three subsets of {1,2,3,4,5,6,7,8,9 } such that the intersection of any two has size 2 and the intersection of all three has size 1 .

Question 33

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 34

Find

Question 35

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 36

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 37

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 38

determine whether the given set is the power set of some set. If the set is a power set, give
the set of which it is a power set.

Question 39

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 40

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.

Question 41

suppose Mark the statement TRUE or FALSE.

Question 42

suppose

Question 43

suppose

Question 44

suppose Mark the statement TRUE or FALSE.

Question 45

suppose Mark the statement TRUE or FALSE.

Question 46

suppose

Question 47

suppose

Question 48

suppose

Question 49

suppose Mark the statement TRUE or FALSE.

Question 50

suppose

Question 51

suppose

Question 52

suppose Mark the statement TRUE or FALSE.

Question 53

suppose Mark the statement TRUE or FALSE.

Question 54

suppose Mark the statement TRUE or FALSE.

Question 55

Suppose ={1,2,3,4,5} . Find .

Question 56

Suppose U={1,2, ... , 9}, A= all multiples of 2, B= all multiples of 3 , and C={3,4,5,6,7} . Find C-(B-A) .

Question 57

suppose

Question 58

suppose

Question 59

suppose Mark the statement TRUE or FALSE.

Question 60

suppose

Question 61

suppose

Question 62

suppose

Question 63

Find A² if A={1, a}

Question 64

determine whether the set is finite or infinite. If the set is finite, find its size.

Question 65

suppose

Question 66

suppose

Question 67

suppose

Question 68

suppose the following are fuzzy sets:

Question 69

suppose

Question 70

suppose

Question 71

determine whether the set is finite or infinite. If the set is finite, find its size.

Question 72

suppose

Question 73

suppose

Question 74

determine whether the set is finite or infinite. If the set is finite, find its size.

Question 75

suppose

Question 76

suppose

Question 77

suppose the following are fuzzy sets:

Question 78

suppose

Question 79

determine whether the set is finite or infinite. If the set is finite, find its size.

Question 80

suppose the following are fuzzy sets: