zyBooks assignment

Question 1

let A be a finite set with the cardinality of n. The cardinality of the power of A is _____

Answer 1

|P(A)| = 2^n

Question 2

let A and B be sets. The intersection of A and B denoted A ∩ B is ________

Answer 2

the set of all elements that are elements of both A and B

Question 3

what is the symbol for intersection?

Answer 3

∩

Question 4

can the intersection operation apply to infinite sets?

Answer 4

yes

Question 5

the union of two sets denoted A ∪ B is _____________

Answer 5

the set of all elements that are elements of A or B

Question 6

if an element is in both sets A and B, is it in the union of the two sets?

Answer 6

yes

Question 7

if an element is in the empty set, it corresponds to _______

Answer 7

false

Question 8

false corresponds to ______

Answer 8

an element being an element of the empty set

Question 9

if an element is in the universal set, it corresponds to _____

Answer 9

true

Question 10

true corresponds to ______

Answer 10

an element being an element of the universal set

Question 11

what is a set identity?

Answer 11

an equation involving sets that is true regardless of the contents of the sets in the expression

Question 12

set identities

Answer 12

paper flashcards

Question 13

an ordered pair of elements indicates that the order of the elements ______

Answer 13

DOES MATTER

Question 14

for two sets A and B, the cartesian product of A and B is denoted ________

Answer 14

A x B

Question 15

the cartesian product of two sets A and B, denoted A x B is ___________

Answer 15

the set of all ordered pairs in which the first entry is in A and the second entry is in B

Question 16

is A x B the same as B x A?

Answer 16

NO, because the order of the pairs is significant

Question 17

if A and B are finite sets, then |A x B| =

Answer 17

|A| * |B|

Question 18

what is an ordered list of three items?

Answer 18

an ordered triple

Question 19

what is an ordered list of four or more items called?

Answer 19

an ordered n-tuple (if a list has 6 items, it is an ordered 6-tuple)

Question 20

what is the cartesian product of A with itself?

Answer 20

A^k = A x A x A, k times

Question 21

if A is a set of characters or symbols, then the elements in A can be written _________

Answer 21

without ( , ). It can be written as A = {xx, xy, yy} (ordered pair example)

Question 22

what is the alphabet for a set of strings?

Answer 22

the characters used in that set of strings

Question 23

what is a binary string?

Answer 23

a string with the alphabet {0, 1}

Question 24

what is a character in a binary string called?

Answer 24

a bit

Question 25

what is an n-bit string?

Answer 25

a binary string with length n

Question 26

what is the empty string?

Answer 26

the unique string with length 0 and is usually denoted by the symbol λ