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

Question 1

Prove or disprove:

Answer 1

True, since

Question 2

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.

Answer 2

Yes,

Question 3

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

Answer 3

False. For example, let A = {1, 2}, B = {1}, C = {2}.

Question 4

For each of the pairs of sets to 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.

Question 5

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 6

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

Question 7

Question 8

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

Question 9

For each of the pairs of sets to 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 10

Prove that by giving an element table proof.

Question 11

Prove or disprove

Question 12

Prove that giving a proof using logical equivalence.

Question 13

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

Question 14

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 15

Prove that by giving a Venn diagram proof.

Question 16

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 17

For each of the pairs of sets to 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 18

Prove that by giving a proof of using logical equivalence.

Question 19

Prove that by giving an element table proof.

Question 20

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

Question 21

Find

Question 22

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

Question 23

Find

Question 24

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 25

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

Question 26

Prove that for all sets S and T .

Question 27

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

Question 28

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

Question 29

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

Question 30

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

Question 31

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 32

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

Question 33

Find

Question 34

suppose A = {x, y} and B = {x, {x}}. Mark the statement TRUE or FALSE.

Question 35

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 36

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

Question 37

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.
(A − C) − (B − C) = A − B

Question 38

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

Question 39

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

Question 40

Find

Question 41

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 42

suppose A = {a, b, c}. Mark the statement TRUE or FALSE.

Question 43

suppose A = {a, b, c}. Mark the statement TRUE or FALSE.

Question 44

suppose A = {a, b, c}. Mark the statement TRUE or FALSE.

Question 45

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 46

suppose A = {x, y} and B = {x, {x}}. Mark the statement TRUE or FALSE.

Question 47

suppose the following are multisets:

Question 48

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 49

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 50

suppose A = {a, b, c}. Mark the statement TRUE or FALSE.

Question 51

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 52

suppose A = {a, b, c}. Mark the statement TRUE or FALSE.

Question 53

suppose A = {a, b, c}. Mark the statement TRUE or FALSE.

Question 54

suppose A = {x, y} and B = {x, {x}}. Mark the statement TRUE or FALSE.

Question 55

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 56

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 57

suppose A = {a, b, c}. Mark the statement TRUE or FALSE.

Question 58

suppose A = {x, y} and B = {x, {x}}. Mark the statement TRUE or FALSE.

Question 59

suppose the following are multisets:

Question 60

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.

Question 61

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 62

suppose the following are fuzzy sets:

Question 63

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 64

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 65

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

Question 66

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 67

suppose the following are multisets:

Question 68

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 69

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

Question 70

suppose the following are fuzzy sets:

Question 71

Find if A={1, a}

Question 72

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 73

suppose the following are fuzzy sets:

Question 74

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 75

suppose the following are multisets:

Question 76

determine whether the set is finite or infinite. If the set is finite, find its size.
P({a, b, c, d}), where P denotes the power set

Question 77

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 78

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.

Question 79

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

Question 80

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.