Question

1. Let S = {a, b, c}. Find a set T such that S ∈ T and S ⊂ T.

2. Let A = {1, 2, ..., 10}. Give an example of two sets S and B such that S ⊂ P(A), |S| = 4, B ∈ S and |B| = 2.

3. Let U = {1, 2, 3} be the universal set and let A = {1, 2}, B = {2, 3} and C = {1, 3}. Determine the following sets: 1. (A ∪ B) − (B ∩ C), 2. A, 3. B ∪ C.

Answer #1

1)Let the Universal Set, S, have 97 elements. A and B are
subsets of S. Set A contains 45 elements and Set B contains 18
elements. If Sets A and B have 1 elements in common, how many
elements are in A but not in B?
2)Let the Universal Set, S, have 178 elements. A and B are
subsets of S. Set A contains 72 elements and Set B contains 95
elements. If Sets A and B have 39 elements...

Let S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }
S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } be the universal set. Let
sets A and B be subsets of S , where: Set A = { 4 , 6 , 10 , 11 ,
12 , 15 , 16 , 18 , 19 , 20 }
Set B = { 1 ,...

Let S and T be nonempty subsets of R with the following
property: s ≤ t for all s ∈ S and t ∈ T.
(a) Show that S is bounded above and T is bounded below.
(b) Prove supS ≤ inf T .
(c) Given an example of such sets S and T where S ∩ T is
nonempty.
(d) Give an example of sets S and T where supS = infT and S ∩T
is the empty set....

let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 9} with A
= {1, 2, 3, 5, 7} and B = {3, 4, 6, 7, 8, 9}
a.)Find (A ∩ B) C ∪ B
b.) Find Ac ∪ B.

Let SS be the universal set, where:
S={1,2,3,...,28,29,30}S={1,2,3,...,28,29,30}
Let sets AA and BB be subsets of SS, where:
Set
A={1,8,13,14,16,17,20,25,27,28}A={1,8,13,14,16,17,20,25,27,28}
Set B={6,7,9,13,14,30}B={6,7,9,13,14,30}
Set
C={5,8,10,11,13,14,15,17,23,25,28}C={5,8,10,11,13,14,15,17,23,25,28}
Find the number of elements in the set (A∩B)(A∩B)
n(A∩B)n(A∩B) =
Find the number of elements in the set (B∩C)(B∩C)
n(B∩C)n(B∩C) =
Find the number of elements in the set (A∩C)(A∩C)
n(A∩C)n(A∩C) =

We denote |S| the number of elements of a set S. (1) Let A and B
be two finite sets. Show that if A ∩ B = ∅ then A ∪ B is finite and
|A ∪ B| = |A| + |B| . Hint: Given two bijections f : A → N|A| and g
: B → N|B| , you may consider for instance the function h : A ∪ B →
N|A|+|B| defined as h (a) = f (a)...

Let S be the set {(-1)^n +1 - (1/n): all n are natural
numbers}.
1. find the infimum and the supremum of S, and prove that these
are indeed the infimum and supremum.
2. find all the boundary points of the set S. Prove that each of
these numbers is a boundary point.
3. Is the set S closed? Compact? give reasons.
4. Complete the sentence: Any nonempty compact set has a....

Let S be a finite set and let P(S) denote the set of all subsets
of S. Define a relation on P(S) by declaring that two subsets A and
B are related if A and B have the same number of elements.
(a) Prove that this is an equivalence relation.
b) Determine the equivalence classes.
c) Determine the number of elements in each equivalence
class.

Set Operations
In questions 7 and 8 Let A = {0, 2, 4, 6}, B =
{0, 1, 2, 3}, and C = {4, 5, 6}. U = {x∈ℤ| 0≤x≤10}
7. Find (A ∪ B) – C’.
8. Find C ∩ (A’ ⊕ B’)
Venn Diagrams
Draw Venn diagrams for the following set operations. Show each
step and label the sets as well as what the diagram is showing Ex:
if the Venn diagram is showing C’, label the rectangle...

1)
a) Let z=x4 +x2y, x=s+2t−u, y=stu2:
Find:
( I ) ∂z ∂s
( ii ) ∂z ∂t
( iii ) ∂z ∂u
when s = 4, t = 2 and u = 1
1) b> Let ⃗v = 〈3, 4〉 and w⃗ = 〈5, −12〉. Find a
vector (there’s more than one!) that bisects the angle between ⃗v
and w⃗.

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