Questions on Logic: Sets and operations answered by real tutors!

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Question 181081: Jose has 4 pairs of slacks, 5 shirts, and 3 sweaters. From how many combinations can he choose if he chooses a pair of slacks, a shirt, and a sweater each day? Please give detail. thanks for your help
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Question 182962: In my math homework it says "use rectangle modelling to solve the following problems". I asked my dad who is a math wiz and he has no idea. One of the questions was 26 x 34. HELP!!!!
Click here to see answer by Edwin McCravy(20060) About Me 

Question 184317: I am having problems with doing Venn Diagrams, I really need your help with this??? Please? Okay, here's the question:
A drug company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 120 people. The results are as follows:
62 liked cherry flavor
74 liked orange flavor
35 liked both flavors
We're asked to construct a Venn Diagram and answer the following:
a.) How many liked only orange flavor
b.) How many liked only cherry flavor
c.) How many like either one or the other or both


This is pretty confusing to me, i'm now sure if i'm making too much out of this or what i'm doing, but I definitely need some help

Click here to see answer by stanbon(75887) About Me 
Question 184317: I am having problems with doing Venn Diagrams, I really need your help with this??? Please? Okay, here's the question:
A drug company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 120 people. The results are as follows:
62 liked cherry flavor
74 liked orange flavor
35 liked both flavors
We're asked to construct a Venn Diagram and answer the following:
a.) How many liked only orange flavor
b.) How many liked only cherry flavor
c.) How many like either one or the other or both


This is pretty confusing to me, i'm now sure if i'm making too much out of this or what i'm doing, but I definitely need some help

Click here to see answer by solver91311(24713) About Me 

Question 184320: Hi! before I go any further with asking a question, I want to say thank you all for helping the students that are totally lost with math or just need a little reassuring, you all have been a blessing in disguise!!!! Thank YOU!!!!!
I have another question on the VENN Diagrams:!!!!!
1.) In a survey of 75 resorts, it was reported that:
34 provided refrigerators in the guest rooms
30 provided laundry services
37 provided business centers
15 provided refrigerators in guest rooms and laundry services
17 provided refrigerators in the guest rooms and business centers
19 provided laundry services and business centers
7 provided all three features.
Construct a Venn Diagram and use it to answer the following questions:
a) How many of the resorts provided only refrigerators in the guest rooms?
b) How many of the resorts provided exactly one of the features?
c) How many of the resorts provided at least one of the features?
d) How many of the resorts provided exactly two of the features?
e) How many of the resorts provided none of the features?

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Question 184510: Set K contains 30 elements, set J contains 46 elements, and 11 elements are common to both sets. Find n ( K U J).
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Question 184509: ) Given U = {18. 19. 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}, A = {21, 23, 25, 27, 29}, and
B = {26, 27, 28, 29}. Find A′ U B′.

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Question 184507: Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set
a) A ∩ B
b) A ∩ C
c) A U C
d) B U C
e) (A U B) ∩ C
f) A U (B U C)
g) (A ∩ B) ∩ C
h) (A ∩ B) U C

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Question 184729: A={x/xEN and 13 B={12, 13,14,15,16,17,18}
For the sets A and B determine whether A=B, A is a subset of B, or B is a subset of A}
For the question I said the A=B, but then I look at it and i'm not sure, I see that the 12 is less than 13, but if it was equal wouldn't it have the less than/equal to sign. I'm confused please helP!

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Question 184843: Please help me with the following problems I have tried and I just don't understand them.
1. Write the following in roster form:
Set N is the set of natural numbers between ten and sixteen

2.Express the following in set builder notation:
Z = {2, 3, 4, 5, 6, 7, 8, 9, 10}
3.For sets A and B, determine whether A = B, A is a subset of B, or B is a subset of A

A = { x| x є N and 13 < x < 18}
B = { 12, 13, 14, 15, 16, 17, 18}
Please Help me Im so confused.

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Question 184847: Please help me with the following question. Ireally need the help my work is due today and I just don't get it.
1.Set K contains 30 elements, set J contains 46 elements, and 11 elements are common to both sets. Find n ( K U J).
2.Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set
a) A ∩ B
b) A ∩ C
c) A U C
d) B U C
e) (A U B) ∩ C
f) A U (B U C)
g) (A ∩ B) ∩ C
h) (A ∩ B) U C
Please help me

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Question 184951: Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set
a) A ∩ B
b) A ∩ C
c) A U C
d) B U C
e) (A U B) ∩ C
f) A U (B U C)
g) (A ∩ B) ∩ C
h) (A ∩ B) U C
Please help with this problem. I can't figure it out and I have tried it many times.

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Question 185481: I am having hard to helping my daughter with this can you please help thank you
suppose C is subset of D and D is a subset of C.
a) If n(c)=5, find n(D)
b) what other relationship exists between sets C and D?

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Question 186680: Set Operations and Venn Diagrams with three sets
Find each of the following sets
(C' backwards U A) U (C' backwards or upsidedown U B')


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Question 186683: U = {1,2,3,4,5,6,7}
A = {1,3,5,7}
B = {1,2,3}
C = {2,3,4,5,6}
Find each of the following sets

(C' upsidedown U A) U (C' upsidedown U B')



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Question 188721: given that U= (a,b,c,d,e,f,g,h,i,j,k), A= (a,b,c,d,e,f) and B= (d,e,i,h) find AUB.
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Question 191247: Several of us in class are having problems with sets, subsets, etc. This question was placed on the board for us to solve. I so need help with this please.
Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}. List the elements of set
(a) A U B
(b) A ∩ B
(c) A′ ∩ B′
(d) A′ U B′
(e) A U B′
(f) (A U B′) ∩ B
(g) (A U B) ∩ (A U B′)

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Question 191857: I just can not figure these out. HELP! Set K contains 50 elements, set J contains 66 elements, and 14 elements are common to both sets. Find n(K U J). We are asked to show the steps.
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Question 191856: I don't think it is in the book but here is one I can not solve, please help. Given U={l,m,n,o,p,q,r,s,t,u,v,w}, A={l,o,p,q,s,t}, B={n,o,r,s,v,w}, and C={l,m,n,q,r,t}, find (A'U C')nB' (n=inverted U).
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Question 191859: This is a question on a quiz I missed. Can someone show me how to figure it out.
1.(4 pts) Given the diagram below, find a) P ∩ Q and b) P U Q I am unable to place the diagram but it is:
U is P,Q,H. Circle I has A & D, Circle II has C, F, & G, and the intersection of I & II has B & E. Thank you from the bottom of my heart.


















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Question 191858: A friend sent me to this web site for help. My question is in my college algebra II class. My mind went blank when I saw this question. Please help. Here goes: Given A={1,2,3,4}, B={3,4,5,6), and C={4,6,7}. Evaluate each set a) AnB,
b)AnC, c) A U C), d.) B U C, e) (AUB)nC, f) AU(BnC), g) (AnB)nC, h) (AnB)UC.
How doe this work. Please show me how this is done. Thank you. (I think she said the "n" was an inverted U.)

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Question 191851: This is a question our instructor gave us and I am at a loss. Please help.
For sets A and B, determine whether A=B, A is a subset of B, or B is a subset of A. A={x|x eN and 13< x < 20} b={14, 15, 16, 17, 18}. (She wants the steps shown). Thanks you for your continued help.

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Question 191886: This was a ten point question I missed on a handout. Can someone help me with it. It did not come from our text book. Thank you in advance.

11.(10 pts) A survey of residents in a small town showed the following:

25 ate beef 13 ate both beef and fish 9 ate all types
28 ate fish 14 ate both fish and poultry 7 ate none of them
30 ate poultry 15 ate both beef and poultry

Draw a Venn diagram. Label your diagram clearly.
Use your diagram to answer the following questions:

(a) How many ate fish, but not poultry or beef?
(b) How many ate poultry and fish, but not beef?
(c) How many ate only beef?
(d) How many ate nothing or only poultry?


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Question 192700:
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Question 193023:
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Question 197527: Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}. List the elements of set
(a) A U B
(b) A ∩ B
(c) A′ ∩ B′
(d) A′ U B′
(e) A U B′
(f) (A U B′) ∩ B
(g) (A U B) ∩ (A U B′)

Click here to see answer by jim_thompson5910(35256) About Me 

Question 197928: I am having a lot of problems trying to figure out these answers and I can't understand how to do them. Can someone please help me a.s.a.p!!!!!!!! Thank you!!!!!!!

For the first one I have to right in detail how the diagram is, because I cannot get the diagram on here.

4. Given the diagram below, find a) P ∩ Q and b) P U Q

The Ven Diagram has "U" on the top left corner of the diagram and "P" on the outside of the left circle. In the left circle are the letters "A" which is at thetop of the inside of the left circle and "D" at the bottom of the inside of the left cirlce. On the circle on the right are the letters "Q" which is on top at the top right of the circle and "H" outside the bottom of the right circle. In the right cirle are the letters "C" on top part of circle, "F" under "C" and "G" under "F" in circle. The intersection of both circles are the letters "B" on top and "E" underneeth the "B".

9. (10 pts) In a survey of 100 consumers, 33 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 34 said they were going to buy a new washer. Of these, 7 were going to buy both a car and a refrigerator, 15 were going to buy a car and a washer, and 9 were going to buy a washer and a refrigerator. Three consumers indicated that they were going to buy all three items.

Construct a Venn diagram, label your diagram clearly.
Use your diagram to answer the following questions:

(a) How many were going to buy only a car?
(b) How many were going to buy only a washer?
(c) How many were going to buy only a refrigerator
(d) How many were going to buy a car and a washer but not a refrigerator?
(e) How many were going to buy none of these items?


10. (4 pts) A survey of a group of people produced the following results: there were 35 people with brown eyes and 24 people with blonde hair. If 14 people had both brown eyes and blonde hair and 27 people had neither, how many people were interviewed?

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Question 198325: Can someone help me figure this out please, I am a bit confused on what to do here!!!! Thanks!!!!!!!!!!

1. (2 pts) Write the negation for the statement below.
Someone in the family makes bread.

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Question 197927: Given U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, o, p, q, s, t}, B = {n, o, r, s, v, w},
and C = {l, m, n, q, r, t}, find (A′ U C′) ∩ B ′.

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Question 197927: Given U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, o, p, q, s, t}, B = {n, o, r, s, v, w},
and C = {l, m, n, q, r, t}, find (A′ U C′) ∩ B ′.

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Question 198366: I really don't understand please help.
1.Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}. List the elements of set
(a) A U B
(b) A ∩ B
(c) A′ ∩ B′
(d) A′ U B′
(e) A U B′
(f) (A U B′) ∩ B
(g) (A U B) ∩ (A U B′

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Question 198532: I am still confused about this problem. I was given help but I am still confused on it. Can someone please help me on this? I will be very greatful on any help that I receive.


2. (2 pts) Let p, q, and r be the following statements:

p: Mary is on the bus.
q: April is in the car.
r: Stan is at the zoo.

Translate the following statement into English: (p v ~ r) -> ~ q

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Question 198633: please help I really need your help!!!!!!!!!!!!!

1.Construct a truth table for ~q -> (~q ^ p).

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Question 201861: Can someone please tell me if this statement is true or false
{3,6,9,12} u {3,9} = {3,6,9,12}

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Question 201853: Persons are classified according to blood type snd Rh quality by testing a blood smaple for the presence of the three antigens: A, B, and Rh. Blood is of type AB if it contains antigens A and B: A if it contains A, but not B; if it contains B, but not A: andO if it contains neither A nor B. In addition, blodd is classified as Rh postive(+) if the Rh antigen is present and Rh negative(-) otherwise. A national report stated that if 1000 people were picked at random and their blood were sampled, the statistics indicated that 490 would contain antigen A, 515 would contain B, 430 would contain Rh, 205 would contain A and B, 140 would contain A and Rh, 160 would contain B and Rh, 205 would contain A and B, 140 would contain A and Rh, 160 would contain B and Rh, and 60 would contain all three. On the basis of this information; determine which of the eight blood classifications is the most plentiful and which is the rarest.
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Question 202480: Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}. List the elements of set

(a) A U B
(b) A ∩ B
(c) A′ ∩ B′
(d) A′ U B′
(e) A U B′
(f) (A U B′) ∩ B
(g) (A U B) ∩ (A U B′)

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Question 202683: Given U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, o, p, q, s, t}, B = {n, o, r, s, v, w},
and C = {l, m, n, q, r, t},
find (A′ U C′) ∩ B ′.
I really need help on this. I have tried and tried to do this Universal Set U stuff but it is very confusing to me... Please help...

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Question 202682: Given U = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}, A = {21, 23, 25, 27, 29}, and
B = {22, 25, 28, 29}. Find A′ U B′.

I am so tired of this stuff I can not get it for some reason this is my 3rd time trying to answer this so I am gonna need some help.. And if u can will you please explain it to me...

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Question 205240: Which of the following numbers can NOT be expressed as the sum of exactly three different numbers from the set : {3,7,15,19,28,33}?
(A)38 (B) 44 (C) 55 (D) 67 (E) None of these

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Question 205795: 2. how many different 4 letter radio station call letters can be made if repeats are allowed and the first letter must be k
a.1000
b.17,576
c.78
d.456,976

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Question 205795: 2. how many different 4 letter radio station call letters can be made if repeats are allowed and the first letter must be k
a.1000
b.17,576
c.78
d.456,976

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Question 210636: A square grid measuring n x n has how many squares in it? Explain your answer.
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Question 212248: Using only 3 nines and no other numbers, create an equation that equals 4. You may use addition, subtraction, multiplying, dividing, and square roots.
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Question 212248: Using only 3 nines and no other numbers, create an equation that equals 4. You may use addition, subtraction, multiplying, dividing, and square roots.
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Question 212261: using only 3 nines, create an equation that equals 8. you can use addition, subtraction, multiplying, dividing, and square roots
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