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

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Question 1121070: Let A = {1,2,3,4} and B = {a,b,c,d} and let f = {(1,a),(2,a),(3,d),(4,c)}. Show that f is a function but f^-1 is not a funtion
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Question 1121072: Show that the mapping f:R-R be defined by f(x) = ax + b where a,b � R, a is not equal to 0 is invertible, define its inverse
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Question 1121649: In a class of 40 students, 17 have ridden an airplane, 28 have ridden a boat, 10 have ridden a train, 12 have ridden both an airplane and a boat. 3 have ridden a train only and 4 have ridden an airplane only. Some students have not yet ridden any of the three modes of transportation and an equal number have taken all the three. How many students have used all the three modes of transportation? How many students have taken only the boat?
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Question 1122483: Consider the set S={a,b,c}. Write down the power set, P(S) of S
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Question 1122536: In a survey of 100 out-patients who reported at a hospital one day, it was found that 70 complained of fever,50 has stomach ache and 30 were injured. All 100 patients had at least one of the complaints and 44 had exactly two of the complaints. How many patients had all the three complaints?

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Question 1122617: There are three student organizations ( A, B and C) in a school. 50 students were asked if they belong to any organizations and the following data were gathered from the survey.
7 belongs to b only
20 belong to c
23 belong to A
4 belong to a and b but not c
8 belong to a and c but not b
14 belong to c but not b
15 belong to a but not b

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Question 1122761: 2,243,6,81,27,...... What is the answer

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Question 1122761: 2,243,6,81,27,...... What is the answer

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Question 1122887: There are three student organizations ( A, B and C) in a school. 50 students were asked if they belong to any organizations and the following data were gathered from the survey.
7 belong to B only
20 belong to C
23 belong to A
5 belong to A and B but not C
8 belong to A and C but not B
14 belong to C but not B
15 belong to A but not B
Draw a venn diagram to determine how many of the student surveyed
(a) belong only to C
(b) do not belong to C
(c) belong to B and C but not A
(d) belong to exactly one organization
(e) do not belong to any organization
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Question 1124955: Find the set A(intercection symbol)C if A={x|1x<4} and C={x|-2
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Question 1125982: find 11 by using 8, 8, 12, 13
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Question 1126125: In a certain city of 15000 families, 3.5% of families who read A but not B look into advertisement, 25% of families who read B but not A look into advertisement and 50% of families who read A and B look into advertisement. It is known that 8000 families read A, 4000 read B and 1000 both A and B.
Find the number of families who look into advertisements.
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Question 1126619: If A = {all prime numbers between 1 and 100}, B = {2,4,6,...,98,100}, and C = {3,6,9,...,96,99}, how many elements does (A union B) intersection C have?
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Question 1127279: Suppose that the universal set U is the set of all odd integers from −5 to 5 inclusively and A={−1,5,−3}. Find Ac.
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Question 1127307: Use sigma notation to write the sum.

+ ... +
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Question 1128497: Write the following in set notation:
1. The set of real numbers greater than 27.
2. The set of all real numbers greater than 8 but less than 73.
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Question 1129419: Need help please. This question makes no sense, and I can't find an example that explains what needs to be done to solve it.
n(U) = 100, n(A) = 24, n(B) = 60, and n(A ∩ B) = 10. Find n(A' ∩ B).
Thank you!
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Question 1129421: -Resubmitted due to typo.
Need help please. This question makes no sense, and I can't find an example that explains what needs to be done to solve it.
n(U) = 100, n(A) = 24, n(B) = 60, and n(A intersection B) = 10. Find n(A' intersection B).
Thank you!
Click here to see answer by itxmenaved(3)

Question 1131781: Can someone please explain this to me? I am completely lost!
Thanks.
U = {a,b,c,d,e,f,g,h,i,j,}
A = {a, c, e, g, i}
B = {b, d, f, h, j}
C = {a, b, d}
1. Determine 𝐴′ ∩ 𝐵
2. Determine (𝐴 ∪ 𝐶) − (𝐴 ∩ 𝐶)
3. Determine Determine 𝐵′ ∩ 𝐶′

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Question 1132302: In a survey of 100 out patients who were reported at a hospital one day found out that 70 complained of fever,50 complained of stomach ache and 30 were injured. All 100 patients had at least one of the complaints and 44 had exactly two of the three complaints. How many patients had all three complaints.

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Question 1133011: Find the complement of the set given that
U = {x | x is in I and −3 ≤ x ≤ 7}.
(Enter your answers as a comma-separated list.)
{−2, −1, 1, 2, 5, 6}
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Question 1134648: Calculate 12 + 19 + 26 + ... + (7n+5), if n=1, 2, 3, ..., 10
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Question 1134754: Find the 20th number of the number pattern; 3, 1, 1/3, 1/9, ...
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Question 1135299: According to students survey, 23 students like history, 26 students liked English, 25 liked mathematics, 15 like math and English, 12 liked history and English. 14 like history and mathematics, 3 liked all of them, and every student liked at least one of the subjects.
a. How many students were in the survey?
b. how many students like only English?
c. How many students like English and history but not mathematics?
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Question 1136042: 1/12, 1/6, 1/4, 1/3, 5/12,what is the next fraction
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Question 1136067: in a school of 50 students were asked to select the choice of their favorite of sports they like 22 like football, 21 like boxing, 25 like table tennis, 7 like football and boxing , 6 like football and table tennis , 1 stundent like none of the sports ,
(i)find the number of the studnets who like all the three sports
(ii)find number of student who like two sports.
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Question 1136798: hi i'm struggling to answer questions concerning minimum and maximum numbers a set can contain,when given a set and a union of two sets.please help,is there a formula to follow or principle
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Question 1137028: List the 4 smallest elements of each set. {y=2x+1, x E(element) natural numbers}
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Question 1139821: 8^3x = 4^6x-1
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Question 1140409: List all elements of each set
The set of all 3-digit numbers made only using digits 2 and 0 (again, each digit can be used more than once.)
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Question 1140918: Hello, my question is about proving a set identity:
Prove (B - A) U ( C-A ) = ( B U C) - A.
I know that I must show (B - A) U ( C-A ) is a subset of ( B U C) - A and ( B U C) - A is a subset of (B - A) U ( C-A ), but I am confused on how I should do this.
I would appreciate some help please.
Click here to see answer by MathLover1(20849)

Question 1145819: As part of his project,a final year student of music, interviewed some undergraduate students, on the type of music they liked listening to;30 liked listening to jazz,20 liked listening to Reggae while 20 also liked to funk.10 students liked listening to jazz and Reggae,10 students liked jazz and funk while 9 students liked to Raggae and funk.if 3students liked listening to all the three music,32 did not like listening to any of the three types of music;find;1. The number that liked listening to jazz only.2: the number that liked listening to funk only;3.the number that liked listening to Raggae only.4.the total number of undergraduate students that were interviewed.
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Question 1145818: at a launch party for 37 Eminem people 25 requested for fried rice, request for salad, while 20 requested for shredded beef.7 people requested for fried rice and shredded beef and 8 people requested for salad and shedded beef.Also 10 people requested for salad only, using a Venn diagram for the three dishes.1. find the number of people that requested for three different dishes.2.find the number of people that requested for two different dishes.Find the number of people that requested for one different dishes.assume that each person requested for at least one dish
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Question 1147569: Given the set {1,2,3,4,5,8,13,21,34} which integers between 30 and 50 cannot be written as a number from the set on it’s own, or as the sum of either two or three numbers from the given set.
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Question 1147623:
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Question 1147618: The odd integers are arranged into sets, each succeeding set continuing from the previous, and containing one more number as follows: {1},{3,5},{7,9,11},{13,15,17,19},... what is the sum of the numbers in the 22nd set?
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Question 1148322: The number of students in PnQ = 62, the number of p =44 and the number of Q =60. How many students are in (PnQ)
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Question 1148322: The number of students in PnQ = 62, the number of p =44 and the number of Q =60. How many students are in (PnQ)
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Question 1148403: A:{1,2,4,6}. B:{10,20}. C:{1,11,12,20}
What is the union of A’ and B
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Question 1149313: In a class of 36 students 25 study chemistry and 22 study mathematics and 25
study physics ,17 study physics and mathematics,18 study physics and
chemistry,15 study one of the three subject Find a)Those who study all three
subject b) only mathematics and chemistry
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035