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

Tutors Answer Your Questions about sets-and-operations (FREE)

Question 1171361: Q1) Let U={a,b,c,d,e,f,g,h,i,j},A={a,b,c,d,e},B={a,b,d,f,g},C={a,d,e} Findl

(A⨁C)\B
(A\C)∩(B\C)
n(A^c∪B^c )

Click here to see answer by CPhill(1959)

Question 1177473: II. A survey was done of 200 8-year olds asking if they like certain types of vegetables (broccoli, carrots, and green beans). The following were obtained.
28 kids only liked green beans.
73 kids liked broccoli.
40 kinds liked broccoli and green beans.
79 kids liked exactly 2 of these vegetables.
12 kinds liked broccoli and carrots, but not green beans.
34 kinds only liked carrots.
104 kids liked carrots or green beans, but not broccoli.
1. How many kids liked carrots, but not green beans?
2. How many kids liked exactly 1 of the three vegetables?
3. How many kids do not like carrots?

Click here to see answer by MathTherapy(10551)

Question 1177472: . 50 people were surveyed about whether they like the ice cream flavors vanilla and strawberry. 20 people liked vanilla, 25 people liked strawberry, and 30 people liked vanilla or strawberry.
1. How many people like vanilla and strawberry?

2. How many people like exactly one of these two flavors?
3. How many people liked strawberry or did not like vanilla?

Click here to see answer by CPhill(1959)

Question 1180160: Anna is a teacher and her cousins are a banker, a salesperson, and an engineer. All of them
sit around a table. Anna sits on Melody's left. Chinky sits at the banker's right. Katherine, who
faces Melody, is not the salesperson. Determine the seating arrangement of the cousins.
Click here to see answer by ikleyn(52772)

Question 1209653: Set a question to prove that (AUB)UC=AU(BUC)
Click here to see answer by CPhill(1959)

Question 1208798: Let A and B be two sets containing 4 and 2 elements respectively. Then the number of subsets of the set AxB, each having at least three elements is
A. 219
B. 228
C. 235
D. 256
Click here to see answer by math_tutor2020(3816)

Question 1208676: Why is the cardinality of the empty set { Ø } equal zero?
Click here to see answer by math_tutor2020(3816)

Question 1208676: Why is the cardinality of the empty set { Ø } equal zero?
Click here to see answer by greenestamps(13198)

Question 1208676: Why is the cardinality of the empty set { Ø } equal zero?
Click here to see answer by ikleyn(52772)

Question 1208679: What is the cardinality of set F?

F = { { Ø }, (x + y), 1/4, 1/3, 1/2, A, B, C, D }

What do I see inside the bigger set?

I see 9 elements.

The cardinality is 9.

Do you agree?
Click here to see answer by Edwin McCravy(20054)

Question 1208677: What is the cardinality of set R?

R = { {1, 2, 3,} {A, B, C} }

I see two sets inside a bigger set. What I see is the key word.

I say the cardinality is 2.

You say?
Click here to see answer by ikleyn(52772)

Question 1208678: What is the cardinality of set B?

B = {pi, e, {x, y, y} }

I see three items in set B.
I see pi, e, and another set containing elements x, y, and z

My answer is 3.
The cardinality is 3.

You say?
Click here to see answer by ikleyn(52772)

Question 1208675: What is the cardinality of set A?

A = {4, 5, 6, 7, 8}

I say 5.

You say?
Click here to see answer by ikleyn(52772)

Question 1208384: Let N be the set of the four gospels. Use the Roster Method to represent the four gospels of the New Testament.

Let N be a set.

N = {Matthew, Mark, Luke, John}

Is this the correct way to apply the roster method in set theory?
Click here to see answer by ikleyn(52772)

Question 1208383: Why can't the elements of a set repeat?

Sample

A = {4, 5, 6, 5} is wrong because number 5 repeats.

Why is it not ok for 5 to repeat?
Click here to see answer by ikleyn(52772)

Question 1208383: Why can't the elements of a set repeat?

Sample

A = {4, 5, 6, 5} is wrong because number 5 repeats.

Why is it not ok for 5 to repeat?
Click here to see answer by Edwin McCravy(20054)

Question 1208382: As I understand it, the cardinality of a set is the number of elements in a set.

Is this right?

Sample

A = {w, x, y, z}

The symbol for cardinality is | A |.

So, for this sample, | A | = 4.

You say?
Click here to see answer by ikleyn(52772)

Question 1208385: Use Set-builder Notation to represent digits 0 to 9.

Let D be a set.

D = {x | x is a digit}

Is this correct in terms of set theory?

Click here to see answer by math_tutor2020(3816)

Question 1208386: Let A and B be sets. If elements of set A are also found in set B, then A is a subset of B.

The textbook writes it this way: A ⊆ B

Sample:

A = {x, x + 1, x + 2}

B = {a, b, c, x, x + 1, x + 2}

I see that the elements in set A are also in set B.

Conclusion: A ⊆ B

You say?
Click here to see answer by math_tutor2020(3816)

Question 1208299: 1 Write the following in set notation:
(a) The set of all real numbers greater than 27.
(b) The set of all real numbers greater than 8 but less than 73.
2 Given the sets S_{1} = \langle2, 4, 6\rangle following statements are true? S_{2} = \langle7, 2, 6\rangle S_{3} = \langle4, 2, 6\rangle and S_{4} = \langle2, 4\rangle which of the
(a) S_{1} = S_{2}
(d) 3 \notin S_{2} deg
(g) S_{1} supset S 4
(b) S_{1} = R
(e) 4 \notin S_{4}
(h) emptyset subset S ?
(c) 5 \in S_{2}
(f) S_{4} subset R
(1) S 3 supset \langle1, 2\rangle
3 Referring to the four sets given in the preceding problem, find:
(a) S_{1} cup S 2
(c) S_{2} cap S 3
(e) S_{4} cap S 2 cap S 1
(b) S_{1} cup S 3
(d) S_{2} cap S 4
(f) S_{1} cup S 1 cup S 4
Click here to see answer by Edwin McCravy(20054)

Question 1208149: If two sets A and B have the same elements, then we say that A = B.
Sample 1
Set A = { 20, 30, 40 }
Set B = { 30, 40, 20 }
I conclude that A = B.
Sample 2
Set A = { red, white, blue }
Set B = { white, blue, red }
I conclude that A = B.
You say?
Click here to see answer by ikleyn(52772)

Question 1208147: The set of digits consists of the following set of numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The textbook tells me that we can denote the set of digits using a Roster Method.
Let D = set of digits
D = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
The book goes on to say that there is a second way to denote a set. That is to use set-builder notation, where the set D of digits is written as D = { x | x is a digit }.
Questions
1. Use the Roster Method to denote the set of even digits.
Let E = set of even digits.
Textbook answer: E = { 0, 2, 4, 6, 8 }.
Why is 0 an element of set E? I thought the whole number 0 is a number without value.
2. Use Set-builder Notation to denote the set of odd digits.
Let O = set of odd digits.
0 = { x | x is an odd digits} = { 1, 3, 5, 7, 9 }
You say?
Click here to see answer by ikleyn(52772)

Question 1208139: Use set-builder notation to denote the set of all even digits.
Let me see.
Let E = set of even digits

E = { x | x is an even digit } = { 0,2,4,6,8 }
Why is 0 an element of set E?
Click here to see answer by math_tutor2020(3816)

Question 1208143: Use set-builder notation to denote the set of the first 4 books in the New Testament.
Question 1
Let N = set of the first 4 books in the New Testament
I say the following:
N = { x | x is one of the first 4 books in the New Testament }
N = { Matthew, Mark, Luke, John }
You say?
Question 2
Use set-builder notation to denote the set of the first 4 books in the New Testament.
Let N = set of all 5 NYC boroughs
I say the following:
N = { x | x represents all 5 boroughs of NYC }
N = { Brookkyn, Bronx, Manhattan, Staten Island, Queens }
You say?
Click here to see answer by math_tutor2020(3816)

Question 1208140: Use the Roster Method to denote the set of all odd digits.
Let O = set of odd digits
O = { 1, 3. 5, 7, 9 }
Questions:
1. Why is 1 an element of set O?
2. Why is 9 an element of set O considering that 9 is not just divisible by 1 and itself?
Click here to see answer by ikleyn(52772)

Question 1208141: If two sets A and B have the same elements, then we say that A = B.

Sample 1
Set A = { 20, 30, 40 }
Set B = { 30, 40, 20 }
I conclude that A = B.
Sample 2
Set A = { red, white, blue }
Set B = { white, blue, red }
I conclude that A = B.
You say?
Click here to see answer by ikleyn(52772)

Question 1206297: Draw a Venn diagram
(A ∩ B) ∪ (A ∩ C)
Click here to see answer by math_tutor2020(3816)

Question 1206297: Draw a Venn diagram
(A ∩ B) ∪ (A ∩ C)
Click here to see answer by mananth(16946)

Question 1206300: Perform the given set operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{4, 5, 8} ∩ {5, 8, 10}
Click here to see answer by ikleyn(52772)

Question 1206195: A group of 2175 students were surveyed about the
courses they were taking at their college with
the following results:
1025 students said they were taking Dance.
1087 students said they were taking History.
1115 students said they were taking Math.
585 students said they were taking History and Math.
501 students said they were taking Math and Dance.
537 students said they were taking History and Dance.
243 students said they were taking all three courses.
Click here to see answer by MathTherapy(10551)

Question 1206204: A group of 2468 students were surveyed about the courses they were taking at their college with the following results:
1140 students said they were taking Psychology.
1244 students said they were taking Dance.
1110 students said they were taking History.
599 students said they were taking Psychology and Dance.
550 students said they were taking Psychology and History.
602 students said they were taking History and Dance.
349 students said they were taking all three courses.
a) How many students took Psychology, History, or Dance?

b) How many students took none of the courses?

c) How many students took Psychology or didn't take History?

d) How many students took Psychology or Dance, but not History?

e) How many students took Psychology & History or took History & Dance?

f) How many students took History and Dance, but not Psychology?

Click here to see answer by ikleyn(52772)

Question 1206205: Given that
U={1,2,3,...,11,12,13}
A={3,5,7,8,9,11}
B= {4,5,6,9,10}
C={1,3,4,5,6,7,10,12}

Determine which elements land in each region of the following Venn Diagram.

ABCI.II.III.IV.V.VI.VII.VIII.

LIST the elements in each of the following regions in set notation: Hint
Region I =
Hint
Region II =
Hint
Region III =
Hint
Region IV =
Hint
Region V =
Hint
Region VI =
Hint
Region VII =
Hint
Region VIII =
Hint
Submit QuestionQuestion 7
Click here to see answer by math_tutor2020(3816)

Question 1206206: A survey was conducted at a local ballroom dance studio asking students what dances they competed in at the most recent competition. Below are the results for the dances Waltz,Bachata, and Mambo:
WaltzBachataMambo278304397205313222217243
a) How many students competed in Waltz, Bachata, or Mambo?

b) How many students competed in Bachata & Mambo, but not Waltz?

c) How many students competed in Waltz or Mambo, but not Bachata?

d) How many students competed in Waltz & Bachata or competed in Bachata & Mambo?

e) How many students competed in none of these three dances?

Click here to see answer by ikleyn(52772)

Question 1205816: Among 70 Jambites, a survey shows that: 23 were taking Physics 25 were taking Biology 22 were taking Chemistry 6 were taking Physics and Biology 7 were taking Biology and Chemistry 8 were taking Chemistry and Physics 2 were taking Physics, Biology and chemistry. (a) How many of the Jambites were taking none of the three sciences? (b) How many were taking just one of the three subjects?
Click here to see answer by ikleyn(52772)

Question 1205085:
Click here to see answer by MathLover1(20849)

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