Let A, B, and C be sets in a universal set U. We are given n(U)...
Let A, B, and C be sets in a universal set U. We are given n(U)
= 63, n(A) = 33, n(B) = 34, n(C) = 28, n(A ∩ B) = 15, n(A ∩ C) =
17, n(B ∩ C) = 14, n(A ∩ B ∩ CC) = 9. Find the following
values.
(a) n(AC ∩ B ∩ C)
(b) n(A ∩ BC ∩ CC)
1. Consider the following situation: The universal set U
is given by: U = {?|? ?...
1. Consider the following situation: The universal set U
is given by: U = {?|? ? ? , ? ≤ 12}
A is a proper subset of U, with those numbers that are
divisible by 4.
B is a proper subset of U, with those numbers that are
divisible by 3.
C is a proper subset of U, with those numbers that are
divisible by 2
a) Using Roster Notation, list the elements of sets U, A, B and
C....
Let
E/F be a field extension, and let α be an element of E that is...
Let
E/F be a field extension, and let α be an element of E that is
algebraic over F.
Let p(x) = irr(α, F) and n = deg p(x).
(a) For f(x) ∈ F[x], let r(x) (∈ F[x]) be the remainder of
f(x) when divided by p(x).
Prove that f(x) +p(x)= r(x)+p(x)in F[x]/p(x).
(b) Prove that if |F| < ∞, then | F[x]/p(x)| = |F|n. (For a
set A, we denote by |A| the number of elements in A.)
1. Let D={1212,1515,1717}, E={1212,1414,1515,1616} and
F={1111,1313,1414,1515,1717}.
List the elements in the set (D∪E)∩F.
(D∪E)∩F=
2. Let...
1. Let D={1212,1515,1717}, E={1212,1414,1515,1616} and
F={1111,1313,1414,1515,1717}.
List the elements in the set (D∪E)∩F.
(D∪E)∩F=
2. Let U = { 1,7,9,11,13,16,17,18,19}, X = {7,11,16,18}, Y =
{7,9,11,13,16}, and Z = { 1,7,9,18,19}. List the members of the
given set, using set braces.
(X∩Y′)∪(Z′∩Y′)
(X∩Y′)∪(Z′∩Y′)=
3. Use the union rule to answer the question.
If n(B) = 16, n(A ∩ B)=5 , and (A ∪ B) =17,
n(A)?
Problem 2.1 Which of the following are sets? Assume that a
proper universal set has been...
Problem 2.1 Which of the following are sets? Assume that a
proper universal set has been chosen and answer by listing the
names of the collections of objects that are sets. Warning: at
least one of these items has an answer that, while likely, is not
100% certain. (i) A = {2,3,5,7,11,13,19} (ii) B={A,E,I,O,U} (iii)
C={√x : x < 0} (iv) D = {1,2,A,5,B,Q,1,V} (v) E is the list of
first names of people in the 1972 phone book in...
Given two sets A and B, the
intersection of these sets, denoted A ∩
B, is...
Given two sets A and B, the
intersection of these sets, denoted A ∩
B, is the set containing the elements that are in both
A and B. That is, A ∩ B =
{x : x ∈ A and x ∈
B}.
Two sets A and B are
disjoint if they have no elements in common. That
is, if A ∩ B = ∅.
Given two sets A and B, the union of
these sets, denoted A ∪ B,...