# Questions on Logic: Subset answered by real tutors!

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 Logic: Subset Solvers Lessons Answers archive Quiz In Depth

Question 746477: How many distinct subsets of
{q,y,k,g} are there?

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There are 4 elements, so there are 2^4 = 16 subsets total.

Question 745149: List all possible subsets of the given set.
I= {5, 6}

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List all possible subsets of the given set.
I= {5, 6}
----
zero elements: null set
1 element: {5},{6}
2 elements: {5,6}
=====================
Cheers,
Stan H.
=====================

Question 743402: 3x times 3y
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3x times 3y = (3*3)*(xy) = 9xy

Question 742939: u-3/4=6 2/3
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u-3/4=6 2/3
-----
u = (20/3) + (3/4)
----
u = (80+9)/12 = 89/12 = 7 5/12
===================================
Cheers,
Stan H.

Question 739528: 7b2+34b-5/b+5
You can put this solution on YOUR website!

Question 737997: what are the subsets of (-9,7)? how do you find the subset?
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what are the subsets of (-9,7)? how do you find the subset?
------------
2 elements --> 2^2 = 4 subsets
----
{} null set
{-9}
{7}
{-9, 7}

Question 737417: Let U = {1,2,3,4,5,6,7}
A = {1,3,5,7}
B = {1,2,3}
C = {2,3,4,5,6}
What are these sets?
2. A ∩(BUC)
4.(A∩B)U (A∩C)
6. C'∩(AUB')
8.(C'∩ A)U(C'∩B')
10. (A∩B∩C)'
12. (B U C)' ∩ A
Thank you for your help in advance, means a lot, since I struggle so greatly with math. :(

You can put this solution on YOUR website!

Let U = {1,2,3,4,5,6,7}
A = {1,3,5,7}
B = {1,2,3}
C = {2,3,4,5,6}
What are these sets?
first find (BUC)- everything that is in either of the sets
(BUC)={1,2,3,4,5,6}
(A∩B)-only the things that are in both of the sets
(A∩B)={1,3,5,7}∩{1,2,3}={1,3}
(A∩C)={1,3,5,7}∩{2,3,4,5,6}={3,5}
C'--"C' is complement", or "not C"; if U = {1,2,3,4,5,6,7} and C = {2,3,4,5,6} , then C'={1,7}
if U = {1,2,3,4,5,6,7} and B = {1,2,3}, then B'={4,5,6,7}
2. A ∩(BUC)
then
A ∩(BUC)={1,3,5,7} ∩{1,2,3,4,5,6}-only the things that are in
both of the sets
A ∩(BUC)={1,3,5}

4.(A∩B)U (A∩C)={1,3} U {3,5}={1,3,5}

6. C'∩(AUB')={1,7}∩({1,3,5,7}U{4,5,6,7} )={1,7}∩({1,3,4,5,6,7} )={1,7}

8.(C'∩ A)U(C'∩B')=({1,7}∩{1,3,5,7})U({1,7}∩{4,5,6,7})=({1,7})U ({7})={1,7}

10. (A∩B∩C)'=({1,3,5,7}∩ {1,2,3} ∩{2,3,4,5,6})'=(1,3}∩{2,3,4,5,6})'=(3)'= {1,2,4,5,6,7}

12. (B U C)' ∩ A=({1,2,3}U{2,3,4,5,6})'∩ {1,3,5,7}=({1,2,3,4,5,6})'∩ {1,3,5,7}={2,4,6}

Question 731622: i have been doing combinations,and i have researched about subsets? and i found out that subsets are 2 to the power n but now i have a question ,given a subset ,how do you find the possible outcomes of choosing a specific number,ie (1,2,3,5,5,6,7,8,9,10,11) ,how many subsets contain the number 5 how many subsets contain exactly three elements, one of which is 3
d. contain exactly five elements, but neither 3 nor

You can put this solution on YOUR website!
The number of subsets with to elements from a set with elements is elements, there are subsets.

How many subsets of {1,2,3,4,5,6,7,8,9,10,11} contain the number 5?
One of those subsets will be {5}, with just one element.
If you remove the number 5 from each of the subsets containing 5, you would get all the subsets of {1,2,3,4,6,7,8,9,10,11} and there is or of those (counting the empty set and the whole 10-element {1,2,3,4,6,7,8,9,10,11} set
That is the number of subsets containing 5, counting {5} and {1,2,3,4,5,6,7,8,9,10,11}.

How many subsets of {1,2,3,4,5,6,7,8,9,10,11} contain exactly three elements, one of which is 3?
Removing 3 from each of those subsets would give you all the subsets of {1,2,4,5,6,7,8,9,10,11} with exactly 2 elements and that is subsets. There are several different combination symbols for that and you know which one you are expected to use.

How many subsets of {1,2,3,4,5,6,7,8,9,10,11} have 5 elements but contain neither 3 not 5?
All of those subsets can be made from {1,2,4,6,7,8,9,10,11} and there is
of them.

Question 731173: Is {3} subset of {1, 2, 4, 5, 6}
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Ans: No
Cheers,
Stan H.

Question 729191: Must show all work!
If A={1, 2, 3, 4, 5, 6, 7, 8}
How many subsets does of A have?

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When a set has n elements, the no. of subsets of the set is 2^n. In set A there are 8 elements so n = 8. Number of subsets is 2^8 = 256

Question 728523: A is the set of whole number factors of 12, and B is the set of whole number factors of 9. Determine
whether the statement B⊆A is true or false. Use a Venn diagram to support your answer.

You can put this solution on YOUR website!
Draw a circle to represent the factors of 12. So the numbers 1, 2, 3, 4, 6, 12 go in this circle.

The question is: Does the circle representing the factors of 9 go completely in the circle we just drew? Surely 1 and 3, which are factors of 9, are also factors of 12. However, 9 is a factor of 9, but it is NOT a factor of 12.

So you'll have a circle that overlaps the previous circle, but a piece of it will be outside of the previous circle. The factors 1,3 go in the piece that's inside the "factors of 12 circle" and the number "9" goes in the piece that's outside the "factors of 12 circle"

So B⊆A is false since not all elements in B are also in A.

Question 728475: Calculate the number of subsets for A={2,4,6,8}
Found 2 solutions by lynnlo, stanbon:
You can put this solution on YOUR website!
Calculate the number of subsets for A={2,4,6,8}
----
Each element is either in or not in any given subset.
----
# of subsets = 4^2 = 16
----------------------------
cheers,
Stan H.

Question 728477: Convert 2312 Base 4 to Base 10
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Convert 2312 Base 4 to Base 10
----
2*4^3 + 3*4^2 + 1*4 + 2
----
= 2*64 + 3*16 + 6
---
= 128 + 48 + 6
======
= 182 (base 10)
===================
Cheers,
Stan H.
==================

Question 727402: convert 287 to base 3
Found 2 solutions by Edwin McCravy, KMST:
Answer by Edwin McCravy(8879)   (Show Source):
You can put this solution on YOUR website!
287 to base 3
We divide 3 into 287, getting 95 with remainder 2. We write the
quotient 95 below and the remainder 2 out to the side, like this:

3)287
95 R=2

Under that, we divide 3 into 95, getting 31 with remainder 2. We
write the quotient 31 below and the remainder 2 out to the side,
like this:

3)287
3)95 R=2
31 R=2

Under that, we divide 3 into 31, getting 10 with remainder 1.  We
write the quotient 10 below and the remainder 1 out to the side,
like this:

3)287
3)95 R=2
3)31 R=2
10 R=1

Under that, we divide 3 into 10, getting 13 with remainder 1.  We
write the quotient 3 below and the remainder 1 out to the side,
like this:

3)287
3)95 R=2
3)31 R=2
3)10 R=1
3 R=1

Under that, we divide 3 into 3, getting 1 with remainder 0.  We
write the quotient 1 below and the remainder 0 out to the side,
like this:

3)287
3)95 R=2
3)31 R=2
3)10 R=1
3)3 R=1
1 R=0

Under that, we divide 3 into 1, getting 0 with remainder 1.  We
write the quotient 0 below and the remainder 1 out to the side,
like this:

3)287
3)95 R=2
3)31 R=2
3)10 R=1
3)3 R=1
3)1 R=0
0 R=1

We are done since the last quotient was 0.

To get the number 287 in base 3, we write
the remainders from bottom to top:

287 in base ten equals 101122 in base 3.

Edwin

You can put this solution on YOUR website!
Dividing 287 by 3 we get 95 for a quotient and .
Dividing 95 by 3 we get 31 for a quotient and .
Dividing 31 by 3 we get 10 for a quotient and .
Dividing 10 by 3 we get 3 for a quotient and .
Dividing 3 by 3 we get for a quotient and .

The answer is in base 3, whose value is

The reason why the repeated division works can be explained through that example like this
The last division tells us that
because 3 ÷ 3 = 1 R0
The previous division tells us that
because 10 ÷ 3 = 3 R1
Putting them both together

The division before that told us that
and that along with
gets us
=
The second division told us that
and that along with
gets us
=

The first division told us that
and that along with
gets us
which means

Question 722677: N-10=11 do you add 10 to each side or subtract 10 from each side
Found 2 solutions by sheldonbbtrocks, Alan3354:
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N-10=11 do you add 10 to each side or subtract 10 from each side
---------------
Try it, see what you get.

Question 721796: what is the proper subset of 0,16,19,1
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There are subsets of any set with elements, hence there are proper subsets of any set with elements. So for your set with 4 elements there are 15 proper subsets. Bottom line: I can't answer your question because you did not provide enough information.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 715177: How many subsets does a set of 18 members have?
You can put this solution on YOUR website!
In general: If a set has n elements, then it will have subsets.

In this case, n = 18, so there are different subsets.

Question 714308: I am having trouble with subsets can you help me and tell me if i am on the right track?: list all the subsets of Q={2,4,6,8,10,12}
here is what I have so far:
{2} {2,4}
{4} {2,6}
{6} {2,8}
{8} {2,10}
{10} {2,12}
{12}

You can put this solution on YOUR website!
List all the subsets that have 0 elements, 1 element, 2 elements, 3 elements, etc until you reach 6 like so

List of Subsets with Six Elements: Empty Set {}

List of Subsets with One Element: {2}, {4}, {6}, {8}, {10}, {12}

List of Subsets with Two Elements: {2, 4}, {2, 6}, {2, 8}, {2, 10}, {2, 12}, {4, 6}, {4, 8}, {4, 10}, {4, 12}, {6, 8}, {6, 10}, {6, 12}, {8, 10}, {8, 12}, {10, 12}

List of Subsets with Three Elements: {2, 4, 6}, {2, 4, 8}, {2, 4, 10}, {2, 4, 12}, {2, 6, 8}, {2, 6, 10}, {2, 6, 12}, {2, 8, 10}, {2, 8, 12}, {2, 10, 12}, {4, 6, 8}, {4, 6, 10}, {4, 6, 12}, {4, 8, 10}, {4, 8, 12}, {4, 10, 12}, {6, 8, 10}, {6, 8, 12}, {6, 10, 12}, {8, 10, 12}

List of Subsets with Four Elements: {2, 4, 6, 8}, {2, 4, 6, 10}, {2, 4, 6, 12}, {2, 4, 8, 10}, {2, 4, 8, 12}, {2, 4, 10, 12}, {2, 6, 8, 10}, {2, 6, 8, 12}, {2, 6, 10, 12}, {2, 8, 10, 12}, {4, 6, 8, 10}, {4, 6, 8, 12}, {4, 6, 10, 12}, {4, 8, 10, 12}, {6, 8, 10, 12}

List of Subsets with Five Elements: {2, 4, 6, 8, 10}, {2, 4, 6, 8, 12}, {2, 4, 6, 10, 12}, {2, 4, 8, 10, 12}, {2, 6, 8, 10, 12}, {4, 6, 8, 10, 12}

List of Subsets with Six Elements: {2, 4, 6, 8, 10, 12}

If you count up the individual sets, you'll find that there are 64 different sets. You can also use the formula 2^n to get 2^6 = 64

So again, there are 64 different possible subsets of {2, 4, 6, 8, 10, 12}

Question 711282: perform the given setoperation let u=(1,2,3,4,5,6,7,8,9,10,)

You can put this solution on YOUR website!
I see the universal set, but where are sets A and B? Also, what operation(s) do you want to perform?

Question 708756: Write the equation for the following relation.
R = {(x, y): (4, 5), (8, 7), (12, 9), (16, 11), . . .}

You can put this solution on YOUR website!
From one point to the next x increases by 4, while y increases by 2.
So, it's a linear equation/relation/function, with a slope of for y as a function of x.
The equation would be .
Substituting the coordinates of point (4, 5)
--> --> -->
So the equation could be or any of the infinity of equivalent equations,
like (obtained by multiplying both sides times 2).
or , or , or .

Question 708260: what are the subsets of {3,5,8,11}
You can put this solution on YOUR website!
The null/empty set is a subset of every set. The other subsets will be all the sets formed from using 1 or more members of the set:
{3}
{5}
{8}
{11}
{3,5}
{3,8}
{3,11}
{5,8}
{5,11}
{8,11}
{3,5,8}
{3,5,8}
{3,8,11}
{5,8,11}
{3,5,8,11} (A set is a subset of itself)

Question 707700: Give an example of a situation where finding the cross product of two sets is useful include two sets and there cross product
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Give an example of a situation where finding the cross product of two sets is useful include two sets and there cross product
----
If an 8 ft tree casts a shadow of 20 ft, how long is
the shadow of a 6 ft man?
Use a proportion:
x/6 = 20/8
x = 6(20/8) = 120/8 = 15 ft.
=================
Cheers,
Stan H.

Question 707436: Evaluate the expression |-22| + |4|
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|-22| + |4| = 22 + 4

|-22| + |4| = 26

Question 707189: all possible subsets of {8,9}
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Hi, there--

The list of possible subsets of {8,9} is:
{8}, {9}, {8,9}, and { }. The symbol { } represents the empty (or null) set.

Mrs.Figgy
math.in.the.vortex@gmail.com


Question 707055: subset of {2,5,7}
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All subsets of {2,5,7}

{2,5,7}
{2,5},{2,7},{5,7}
{2},{5},{7}
{ }

Note: { } is the empty set

Question 706378: please help me solve the the given set operations 1,2,3,4,5,6,7,8,9,0, enter answer separated bt commas, {1,3,7,} U 2,5,8} is it 1,2,3,5,7,8

Question 706338: List all numbers from the given set B that are members of the given Real Number subset.
B={1,√7,-9,0,6/7,√16,0.4 (with a line over the 4),0.24} rational numbers

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Rational numbers can be expressed as p/q where both p and q are integers and q is not 0.

1 can be expressed as 1/1. It is rational.

is not a rational number. There is no way to express it as p/q - see proof at the end.

9 is rational = 9/1 (any integer is rational). 0 is rational (0/1).

By definition, 6/7 is rational (p=6 and q=7)

= 4 or -4, so it is rational (4/1 or -4/1).

That line over the 4 means the 4 repeats forever...it is a non terminating decimal that repeats. Non terminating, repeating decimals are rational.

It's easy to find the fraction:

A: x = .4(repeating)

B: 10x = 4.4(repeating) (multiplied A by 10.)

Subtract: B-A = 9x = 4

Solve for x...x=4/9.

.24 is a terminating decimal. Terminating decimals are rational. .24 is 24/100 or simplified 6/25.

The only number from B that isn't a rational number is .

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

Proof by contradiction: suppose that root 7 (I'll write sqrt(7)) is a rational number, then we can write sqrt(7)=a/b where a and b are integers in their lowest form (ie they are fully cancelled). Then square both sides, you get 7=(a^2)/(b^2) rearranging gives (a^2)=7(b^2). Now consider the prime factors of a and b. Their squares have an even number of prime factors (eg. every prime factor of a is there twice in a squared). So a^2 and b^2 have an even number of prime factors. But 7(b^2) then has an odd number of prime factors. But a^2 can't have an odd and an even number of prime factors by unique factorisation. Contradiction X So root 7 is irrational.

Question 705937: for the given set, first caclulate the number of subsets for the set then calculate the number of proper subsets {15, 10, 16, 20, 19}
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The general formula for number of subsets is and the number of proper subsets is , where is the number of elements.
if given set { ., , , , .}, we can see that the number of elements is
so, the number of subsets is

and the number of proper subsets is

Question 705548: I am having problems understanding how to show the answer to this problem. If
If n(A)= 15, n(A n B)=5, and n(A u B)=30, then what is n(B)? I know the answer is 20, I just am not sure of how I got the result. Can you help me?

You can put this solution on YOUR website!
n(A) is the population of "A"'s
That includes:
- n(A n 'B) (A and not B)
- n(A n B) (Both A and B)
So, if n(A n B)=5 and n(A)=15:
n(A n 'B)= 10
Thus is n(A u B)=30 and n(A n 'B)=10:
n(B)= 20
-------------------------------------
Think of this as a venn diagram
The left two sections would be called n(A)= 15
The middle section would be n(A n B)=5
Thus the left section would be n(A n 'B) = 10
Finally of both the far left and the far right sections n(A u B)=30;
n(A u B) - n(A n 'B) = n(B)
30 - 10 = 20

Question 705097: 5x-4y=-6
X-2y=-6

You can put this solution on YOUR website!
5x-4y=-6
X-2y=-6
----------
Do you have a question?

Question 703691: List all of the subsets of {A, B, C}. For subsets with more than one element, list the elements in alphabetical order, separated by commas.
You can put this solution on YOUR website!
List all of the subsets of {A, B, C}. For subsets with more than one element, list the elements in alphabetical order, separated by commas.
Subsets with one element
{A}, {B}, {C}
Subsets with two elements
{A, B}, {A, C} {B, C}
Subsets with three elements
{A, B, C}
I almost forgot, the sets with no elements, i.e. the empty set is also a subset!
{}
So all the subsets would be:
{}, {A}, {B}, {C}, {A, B}, {A, C} {B, C},{A, B, C}

Question 701168: 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 or Ø for the empty set.)

{1, 3, 5} {2, 4, 9}

Question 700887: Which of the following sets has only
one subset.
A) {Y, Z}
B) {Y}
C) {0}
D) { }

You can put this solution on YOUR website!
Every set has the empty set as a subset. So if a set has 1 element, like {0}, then it will have 2 subsets: itself and the empty set, which is denoted { }.

So if a set has only one subset, then this set must be the empty set. There is no other set that fits this description.

So the answer is D) { }

Question 696391: (x+y+z)^2=?
You can put this solution on YOUR website!

let q = x+y

plug in q = x+y

Question 696415: Which of the following is not an equal set?
i) A = {4, 3, 2, 1 } B= {1, 3, 2, 4 }
ii) A ={ 2, 3 } , B = { 3, 2 }, C = { x:x2 – 5x – 6 =0 }
iii) A = { 4, 5 ) B = { 5, 4 }
iv) A = { 6, 7, 8 } B= { Six, seven, eight }

You can put this solution on YOUR website!
i) A = {4, 3, 2, 1 } B= {1, 3, 2, 4 }.........order doesn't matter
ii) A ={ 2, 3 } , B = { 3, 2 }, C = { x:x2 – 5x – 6 =0 }...find solutions:

as you can see, solutions are and ; so,
iii) A = { 4, 5 ) B = { 5, 4 }......
iv) A = { 6, 7, 8 } B= { Six, seven, eight }........

so, the following is not an equal set:
ii) A ={ 2, 3 } , B = { 3, 2 }, C = { x:x2 – 5x – 6 =0 }

Question 696414: Which of the following is not an equal set?
i) A = {4, 3, 2, 1 } B= {1, 3, 2, 4 }
ii) A ={ 2, 3 } , B = { 3, 2 }, C = { x:x2 – 5x – 6 =0 }
iii) A = { 4, 5 ) B = { 5, 4 }
iv) A = { 6, 7, 8 } B= { Six, seven, eight }

Answer by Edwin McCravy(8879)   (Show Source):
You can put this solution on YOUR website!
Which of the following is not an equal set?
i) A = {4, 3, 2, 1 } B= {1, 3, 2, 4 }
Those are equal sets because the order in which they are written
does not matter.


ii) A ={ 2, 3 } , B = { 3, 2 }, C = { x:x² – 5x – 6 =0 }
A and B are equal sets because the order in which elements are written
does not matter. Let's solve the equation in C to find out what
elements it has:

x² - 5x - 6 = 0
(x+1)(x-6) = 0
x+1 = 0;  x-6 = 0
x = -1;   x = 6

Aha!  That's the set C = {-1, 6}, not the set (2, 3}.

[Note:  If it had been C = { x:x² – 5x + 6 =0 }, with +6 instead
of -6, C would have been the same set as A and B]


iii) A = { 4, 5 ) B = { 5, 4 }
Those are equal sets because the order in which they are written does not matter.


iv) A = { 6, 7, 8 } B= { Six, seven, eight }
Those are equal sets because the numerals for the numbers and the words
for the numbers are both symbols for the same numbers.

Edwin

Question 683991: Given the diagram below, find PUQ. Write in correct set notation.

Answer by Edwin McCravy(8879)   (Show Source):
You can put this solution on YOUR website!
What diagram below?

Question 676884: what are all the subsets of 3,5,7
You can put this solution on YOUR website!

all the subsets of {3,5,7} are:
{ }, {3}, {5}, {7}, {3,5}, {3,7}, {5,7}, {3,5,7}
so, there are subsets of {3,5,7}

Question 675760: If n(A) = 40, n(B) = 15, and n(A ∩ B) = 5, find n(A u B).

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If n(A) = 40, n(B) = 15, and n(A ∩ B) = 5, find n(A u B).
---------
n(AuB) = n(A)+n(B)-n(A and B)
-------
n(AuB) = 40 + 15 - 5
------
n(AuB) = 50
====================
cheers,
Stan H.

Question 674467: V-5/6=-7/8
You can put this solution on YOUR website!
V-5/6=-7/8
----
V = (5/6)-(7/8)
---
V = (40-42)/48
----
V = -2/48
---
V = -1/24
============
Cheers,
Stan H.

Question 672623: n(B)=20, n(A^B)=5, n(AvB)=30 find n(A)
You can put this solution on YOUR website!
Just to be clear, in this context, A^B means "set A intersect set B"

n(A^B) = n(A) + n(B) - n(AvB)

5 = x + 20 - 30

5 = x - 10

5+10 = x

15 = x

x = 15

So n(A) = 15

Question 672391: how many distinct subsets are there of a set having six elements?