course Mth 151
Math 151 Assignment 2 sections 2.3-2.52.3
3. The difference of A and B A
5. The Cartesian product of A and B E
6. The difference of B and A D
9. Y U Z= {a,b,c,d,e,f} Y= {a,b,c} Z={b,c,d,e,f} if it is a union the two are joined to make {a,b,c,d,e,f}
10. Y intersect Z= b,c (intersection of a set indicates what the sets have in common.
12. Y intersect U= U being the universal set and this problem being an intersection of sets which mean what is in common the answer is{a,b,c}
15. X intersect Y= since x and y are complements it is what is outside their sets that is the answer. {d,f}
18. Y intersect {XUZ}={a,g}
20. {X U Y} U Z={d,f} (This is because it is what is outside of X and Y The elements not in X or Y are {d,f}
21. {Z U X} intersect Y={a}
24.Y-X= {e,g}
25. X intersect {X-Y}={e,g}
27. X-Y={d,f} After X is excluded and Y is subtracted the only part of the universal set left is {d,f}
30.{X intersect Y} intersect {Y intersect X} = {d,f}
33. {C-B} U A= The set of all elements that are in C but not in B, or are in A.
35. {A-C} U {B-C}= The set of all elements that are in A but not in C, or in B but not in C.
36. {A intersect B} UC= The set of all elements that are not in A or B or C.
39. T={l,b}
40. T intersect A= The set of all elements in A and B
42. T intersect A= {e,c} Set of all elements not contained in A
45. {C-A}=The set of all tax returns filed in 2005 without itemized deductions.
48.{C intersect A} intersect B=The set of all tax returns filed in 2005 and the set of all tax returns with itemized deductions but not the set of tax returns showing business income.
50. A subset {A intersect B}= Always True
51.{A intersect B} subset A= Always True
54.n{A U B}=n{A} + n{B}-n{A intersect B} Not always True
55. Find X U Y={1,3,5,2}
Y U X={1,2,3,5}
C. For any sets X and Y, X U Y= Y U X
57. Find X U {Y U Z}= {1,3,5,2,4}
b.Find {X U Y} U Z={1,3,5,2,4}
C.For any sets X,Y, and Z, X U (Y U Z}={X U Y} U Z
60.Find {X intersect Y}={5}
b. X U Y={4}
C. For any sets X and Y or X and Y
63.{3,2}=5-2, 1+1= True
65. {6,3}={3,6}
False
66.{2,13}={13,2}
False
69. {(1,2), (3,4)} = {(3,4)(1,2)}
True
70.{(5,9), (4,8),(4,2)={(4,8),(5,9),(4,2)}
False
72. A= {3,6,9,12}, B={6,8}
AXB not equal to BXA
75. n(A X B)=6, n (B X A)=6
78. n (A)=13 and n(B) =5 (A X B is not equal to (B X A)
80.If n(A X B) = 300 and n(B) =30 find n(A)? 10
U={a,b,c,d,e,f,g}
A={b.d.f.g}
B={a,b,d,e,g}
81. A= f,
B= a,e
Both A & B in common= d,b,g
84. A U B= This is the set of all elements belonging to either set. Both sides of the diagram would be colored in, as would the center.
85.A U B=This means all elements not in A, but in set B and the area in the center which is the area they would have in common would be colored in but not A.
87.B U A= This means all parts not in set B so, A and the center where the area for what they have in common would be colored in.
90.A intersect B= All parts of the set not in B which means only A is colored in, not B or the center where the common area is. Only set A is colored.
93. U=U is the universal set. So, if it is U that is all things outside the universal set which usually contains all possibilities. Neither side nor the center is colored in. It is blank. The answer is Empty set.
95.
U={m,n,o,p,q,r,s,t,u,v,w}
A={m,n,p,q,r,t }
B= {m,o,p,q,s,u}
C={m,o,p,r,s,t,u,v}
A= n
B= Has nothing by itself.
C=v
A&B=q
A&C=r,t
B&C=o,s,u
A,B,&C=r,t,m,p,o,s,u
96.
U= {1,2,3,4,5,6,7,8,9}
A={1,3,5,7}
B={1,3,4,6,8}
C={1,4,5,6,7,9}
A=7
B=8
C=9
A&B= 3
A&C=5,7
B&C=4,6
A,B,&C=1
U=2
99. {A intersect B} U C
The venn diagram would be colored in in A,B and the shared areas of A,B,& C but not the area of C which is not shared.
100. {Aintersect B} intersect C
In this example the shared portions ofA, B and C are colored in and A is uncolored and the parts of B and C which are not part of the common area between sets are not colored either.
102.{A U B} UC=
All areas of the diagram are colored in.
105. {A intersect B} intersect C
Only A is colored in and no shared areas.
108. {A intersect B} U C
A is colored in in the diagram B & C are not also the shared areas should not be colored in.
111. In this diagram A & B are colored in. The common area is not. This is written as:
{A U B} {A intersect B}
114. In this problem only A is colored in. B and C and the common areas are not. This is written as:
{A intersect B} intersect C
115. The common area between A & B was colored in but not the common areas of A,or C or B or C this is written as:
{A intersect B} intersect C
117.A=A-B written as {A intersect B}-C
120. A= empty set A= empty set
123. A intersect empty set=A
A= empty set
125. AUA= empty set
A= empty set
126.A intersect A= empty set
For A intersect A to equal empty set A must be an empty set.
129.{A intersect A} = empty set
This is always true
130. {A U A}=U
If A is joined with A then the items in set A are not for consideration. If U is = to A then U would have to equal the empty set.
132. {A U B} subset of A
Always true
135. {AU B} = A intersect B
Same as A intersect B= AUB and A U B = A intersect B
DeMorgans Law (always true)
138. If Q= {X\X is a rational number and H = {x|X is an irrational number describe each set.
Q U H would have the parts of the set that did not intersect colored in.
Q intersect H would have only the common areas colored in, not Q itself or H itself.
EXERCISE 2.4
3. In #3 (a) =1, (b) =3, (c) = 4, (d)= 0, (e)=2,(f)=10, (g)=2, (h)=5
5. Find the value of n(A UB) if n(A) =8 , n(B) =14, and n(A intersect B)=5
Solution to this problem is: Since A=8 and B=14 which would =22 however 5 items intersect between A and B and are shared but are part of the other two sets and not to be counted twice. Solution is: (17).
6. Find the value of n(A U B), if n(A)=16, n(B)=28, and n(A intersect B)=9
Solution: A U B stands alone as values because they are unions. So (A) = 16 and (B) = 28,
16+28= 44. However, there are 9 common or shared items between (A) and (B) these items are not to be counted twice since they are shared. So, 44-9=35. Final answer is:35.
9. Find the value of n(A) if n(B)=35, n(A intersect B)=15 and n(A U B)=55
Answer: 35
10. Find the value of n(B) if n(A) =20, n(A intersect B)=6 and n(A U B)=30
In this case( A)=20 , There are 6 in common between A and B so in order for the answer to be 30 (B) is +10. The 6 in common are not counted.
12. n(U)=43, n(A)=25, n(A intersect B)=5, n(B)=30
A=25, B= was worth 30 but is not considered and counts nothing or empty set. A intersect B is a common area and 5 items are common to A and B.
15. n(A)=57, n(A intersect B)=35, n(A U B)=81, n(A intersect B intersect C)=15, n(A intersect C)=21, n(B intersect C)=25, n(C)=49, n(B)=52
A=16, A&B=20, B=14,B&C=10, A,B,C=15, A&C=6, C=18
18.n(A intersect B)=21, n(A intersect B intersect C) =6, n(A intersect C)=26,n(B intersect C)=7, n(A intersect C)=25, n(C)=40 , n(A intersect B intersect C)=2
20. (a)8
(b) 7
(c) 15
21.
(a) 18
(b) 15
( c ) 20
(d) 5
24. The list shows the preferences of 102 people at a fraternity party:
(a) 3
(b)96
( C )95
(d) 96
(e) 94,95,96
25.
(a) 37
(b) 22
( c ) 50
(d) 11
(e) 25
(f) 11
27.
(a) 31
(b) 24
( c ) 11
(d)45
30.
33.Yes, You must make a 3 circle venn diagram and abbreviate the beverages so you can tell what they are, however if this system is used you can keep up with who likes what exclusively and what their common tastes are.
Not always true
Exercise 2.5
3. {x|x is a natural number} A
5. {X|X is an integer between 5 and 6} F it is both even and odd.
6. {X|X is an integer that satisfies X to the second =100} C
9. {a,d,d,I,t,I,o,n} and {a,n,s,w,e,r}
a and a correspond. n and d correspond. i and s correspond. t and w correspond. o and e correspond. n and r correspond.
{a d i t o n}
{a n s w e r}
10. {Reagan, Clinton, Bush}
{Nancy, Hillary, Laura}
Reagan corresponds to Nancy. Clinton Corresponds to Hillary. Bush corresponds to Laura.
12.{9,12,15,
36}
The cardinal number for the set above is 10.
{9,12,15,18,21,24,27,30,33,36}
15.{300,400,500,
..}
N0
This is an infinite set and is represented by (N0)
18. {X|X is an even integer} (2)
This can be any even numbered positive or negative number.
20. {b,a,l,l,a,d}
Cardinal number is 6.
21.{Jan,Feb,Mar,
.,Dec}
Cardinal number is 12.
9
Mike Myers and Madonna
Austin Powers and Eva Peron
25. {u,v,w}, {v,u,w}
Both
27. {X,Y,Z}, {x,y,z}
Equivalent
30. {X|X is a positive rational number}, {X|X is a negative rational number}
They can be equivalent if they hold the same number of items.
33. { 1,000,000, 2,000,000, 3,000,000,
,1,000,000n,
}
{1, 2, 3,
, n,
}
35. {2,4,8,16,32,
,2n,
}
{1,2,3,4, 5,
,n
}
36.{-17,-22, -27,-32,
}
{-1,-2,-3,-4,
}
Indefinite sets represented as N0
39.I A is an infinite set and A is not equivalent to the set of counting numbers , then n(A)=c
This statement is not always true.
40. If A U B are both countably infinite sets then n(A U B ) = N0
This is a true statement.
42. |
|
| |
-5 -4 -3 -2 -1 0 1 2 3 4 5
They are infinite. They will continue regardless of how they began.
45. {3/4, 3/8, 3/12, 3/16,
,3/4n,
}
{3/8, 3/12, 3/16, 3/20,
,4n +4,
}
48. {-3,-5,-9,-17,
}
{-3,-5,-17,
}
All elements are present but -9. That makes it a proper subset.
50. Explain how the correspondence suggested in example 4 shows that the set of real numbers between 0 and 1 is not countable.
A real number is any number which can be expressed as a decimal. Decimals, can be infinite.
51. Achilles had to continue to return to the starting place. Tortoise kept going.
You have not used the q_a_ and query programs as instructed, and you have not included sufficient information committee to properly evaluate your work here. While I cannot accurately evaluate your work, I can say that you clearly have at least an adequate understanding of this material and I don't expect that you will have serious problems on the Chapter 2 test.