zyBooks assignment Flashcards
for class when we had the snow day
let A be a finite set with the cardinality of n. The cardinality of the power of A is _____
|P(A)| = 2^n
let A and B be sets. The intersection of A and B denoted A ∩ B is ________
the set of all elements that are elements of both A and B
what is the symbol for intersection?
∩
can the intersection operation apply to infinite sets?
yes
the union of two sets denoted A ∪ B is _____________
the set of all elements that are elements of A or B
if an element is in both sets A and B, is it in the union of the two sets?
yes
if an element is in the empty set, it corresponds to _______
false
false corresponds to ______
an element being an element of the empty set
if an element is in the universal set, it corresponds to _____
true
true corresponds to ______
an element being an element of the universal set
what is a set identity?
an equation involving sets that is true regardless of the contents of the sets in the expression
set identities
paper flashcards
an ordered pair of elements indicates that the order of the elements ______
DOES MATTER
for two sets A and B, the cartesian product of A and B is denoted ________
A x B
the cartesian product of two sets A and B, denoted A x B is ___________
the set of all ordered pairs in which the first entry is in A and the second entry is in B
is A x B the same as B x A?
NO, because the order of the pairs is significant
if A and B are finite sets, then |A x B| =
|A| * |B|
what is an ordered list of three items?
an ordered triple
what is an ordered list of four or more items called?
an ordered n-tuple (if a list has 6 items, it is an ordered 6-tuple)
what is the cartesian product of A with itself?
A^k = A x A x A, k times
if A is a set of characters or symbols, then the elements in A can be written _________
without ( , ). It can be written as A = {xx, xy, yy} (ordered pair example)
what is the alphabet for a set of strings?
the characters used in that set of strings
what is a binary string?
a string with the alphabet {0, 1}
what is a character in a binary string called?
a bit
what is an n-bit string?
a binary string with length n
what is the empty string?
the unique string with length 0 and is usually denoted by the symbol λ
