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#26 Re: Help Me ! » Domain in Set-builder Notation » 2024-09-08 08:38:15

harpazo65
Bob wrote:

Yes, OK.

I would prefer

Bob

I don't know how to use LaTex. By the way, I don't have a computer or a laptop. Learning LaTex with a cell phone is a nightmare in terms of typing all the details carefully.

#27 Re: Help Me ! » Find (B U C)^c » 2024-09-08 08:36:39

harpazo65
Bob wrote:

Again we have a rogue 6 in C.

Bob

Ok. I better pay close attention when typing my elements into the sets.
What do you mean by "rogue 6"?

#28 Re: Help Me ! » Find B^c ∩ C^c » 2024-09-08 08:35:24

harpazo65
Bob wrote:

Yes, that's ok.  But you have typed

C = {1, 3, 4, 6}

  That 6  cannot be an element as it's not in the universe.  Fortunately it doesn't effect your answer.

Bob

Really? Why does 6 not effect my answer? That's a bit weird.

#29 Re: Help Me ! » Definition of Complement » 2024-09-08 08:34:04

harpazo65
Bob wrote:

A set and its complement divide the 'universe' into two non overlapping sets with no elements left out of being in one or the other. So when you unite them you get everything, ie the universe.

And when you look to find what's in both a set and its complement you find nothing hence the empty set.

Normally when I'm showing union and intersection in a picture I draw two overlapping circles (inside a rectangle for the universe). But for a set and its complement a better picture is a rectangle for the universe divided by a single border making the two sets that don't overlap and together make the whole of the universe rectangle.

Bob

I didn't know this information. This reply makes good study notes. I think set theory is worth exploring in the near future.

#30 Re: Help Me ! » Find A^c » 2024-09-08 08:32:29

harpazo65
Bob wrote:

Me too. smile

Bob

What a wonderful surprise. My textbook is not a set theory book. One day, I want to get deeper into this course.

#31 Re: Help Me ! » Find B ∩ (A U C) » 2024-09-08 08:30:44

harpazo65
Bob wrote:

Yes, that's got it!

Bob

Great news! I do my best to show math work.

#32 Help Me ! » Roster Method » 2024-09-08 02:50:53

harpazo65
Replies: 2

Given x, x + 2, x + 4, x + 6, and x + 8, use the Roster Method to represent the given list of expressions.


Let E = set if expressions given.


E = {x, x + 2, x + 4, x + 6, x + 8}

#33 Help Me ! » Domain in Set-builder Notation » 2024-09-08 02:44:42

harpazo65
Replies: 4

Given 2/(x - 2) and (x - 2)/(x + 2), find the domain. Express domain in set-builder notation.


For 2/(x - 2):

x - 2 = 0

x = 2

D = {x | x cannot = 2}

For (x - 2)/(x + 2):

x + 2 = 0

x = -2

D = {x | x cannot = -2}

#34 Help Me ! » Find (B U C)^c » 2024-09-08 02:38:06

harpazo65
Replies: 4

Let (B U C)^c = the complement of B union C.

U = {0, 1, 2, 3, 4, 5}

B = {2, 3, 4}

C = {1, 3, 4, 6}

B U C = {2, 3, 4} U {1, 3, 4, 6}

B U C = {1, 2, 3, 4, 6}

(B U C)^c = {0, 5}

I believe this to be right.

#35 Help Me ! » Find B^c ∩ C^c » 2024-09-08 02:32:43

harpazo65
Replies: 4

Given U = {0, 1, 2, 3, 4, 5}, B = {2, 3, 4}, and C = {1, 3, 4, 6}, find
B^c ∩ C^c.

B^c = {0, 1, 5}

C^c = {0, 2, 5}

B^c ∩ C^c = {0, 1, 5} ∩ {0, 2, 5}

B^c ∩ C^c = {0, 5}

I believe this to be true.

#36 Help Me ! » Definition of Complement » 2024-09-08 02:22:42

harpazo65
Replies: 2

Definition of complement states:

If A is a set, then the complement of A, denoted A^c, is the set consisting of all the elements in the universal set that are not in set A.

It follows that from the definition of complement that A U A^c = U, where U is the universal set. It also follows that A ∩ A^c = null set or Empty set.

Why is this the case?

#37 Help Me ! » Find A^c » 2024-09-08 02:17:16

harpazo65
Replies: 2

If A is a set, then the complement of A, denoted A^c, is the set consisting of all the elements in the universal set that are not in set A.

Let U = universal set

U = {a, b, c, d, e, f, g}

A = {e, f, g}

Find A^c.

Find A^c = {a, b, c, d}

I believe this to be right.

#38 Re: Help Me ! » Set-Builder Notation » 2024-09-08 00:49:26

harpazo65
Bob wrote:

The first is correct for set builder notation. Your second answer is the roster answer.

Bob

That's exactly what I thought. I will post a few more basic set theory questions later on today.

#39 Re: Help Me ! » Roster Method » 2024-09-08 00:48:08

harpazo65
Bob wrote:

Yes that's right. I've never heard it called the roster method though.  Always good to learn something new.

Bob

Roster Method is the term used by Michael Sullivan in his College Algebra Edition 9 textbook. He is a famous mathematician and professor. I think he is retired by now.

#40 Re: Help Me ! » Find B ∩ (A U C) » 2024-09-08 00:18:33

harpazo65
Bob wrote:

I should find A U C first.

A U C = {0, 1, 2, 3, 4, 5} U {2, 4, 6, 8, 10}

A U C = {2, 4}

Yes you should but the union is {0,1,2,3,4,5,6,8,10}

Bob

Yes, my bad. A U C means set A union or united with set C. All the elements of set A united with all the elements of set C.

I then need to find find B intersected with A U C.


B ∩ (A U C) = {6, 7, 8, 9, 10}  ∩ {0, 1, 2, 3, 4, 5, 6, 8, 10}

B ∩ (A U C) = {6, 8, 10}

I hope this is correct now.

#41 Re: Help Me ! » Find A ∩ B » 2024-09-08 00:11:50

harpazo65
Bob wrote:

It is correct.

Bob

Ok. I guess it was just pure luck at my end. The textbook begins with basic set theory. It is not a set theory book.

#42 Re: Help Me ! » Find A U B » 2024-09-08 00:10:14

harpazo65
Bob wrote:

Yes, that's correct.

Bob

Oh, good. I had my doubts here.

#43 Help Me ! » Set-Builder Notation » 2024-09-07 13:12:03

harpazo65
Replies: 2

A second way to denote a set is to use Set-builder Notation, where the set D of digits is written as D = { x | x is a digit}, is we are talking about digits.


We know the digits are single numbers 0 to 9.

Use set-builder notation to represent the set of even digits.

Let E = set of even digits.


E = {x | x is an even digit}
Is this correct?

How about E = {x | x is an even digit} = {2, 4, 6, 8}?

Which one is correct?

#44 Help Me ! » Roster Method » 2024-09-07 13:02:38

harpazo65
Replies: 4

If we use the symbol D to denote the set of NYC boroughs,  then we can write D = {Brookkyn, Queens, Manhattan, Bronx, Staten Island}. This method of denoting a set is called the Roster Method.


Use the Roster Method to denote the first 4 books in the New Testament.


Let N = the set of the first 4 books in the New Testament.


N = {Matthew, Mark, Luke, John}

I think this is correct.

#45 Help Me ! » Find B ∩ (A U C) » 2024-09-07 12:56:22

harpazo65
Replies: 4

Note:

B ∩ (A U C) means set B intersected with set A union with set C.

Set A = {0, 1, 2, 3, 4, 5}

Set B = {6, 7, 8, 9, 10}

Set C = {2, 4, 6, 8, 10}


Find B ∩ (A U C).

I should find A U C first.

A U C = {0, 1, 2, 3, 4, 5} U {2, 4, 6, 8, 10}

A U C = {2, 4}

B ∩ (A U C) = {6, 7, 8, 9, 10} ∩ {2, 4}


B ∩ (A U C) = null set or empty set

I think this is correct.

#46 Help Me ! » Find A ∩ B » 2024-09-07 12:49:25

harpazo65
Replies: 2

If A and B are sets, the intersection of A with B, denoted
A ∩ B, is the set consisting of elements that belong to both A and B.

Given set A = {w, x, y, z} and set B = {e, pi, x, y}

A ∩ B = {w, x, y, z} ∩ {e, pi, x, y}

A ∩ B = {x, y}

I think is correct.

#47 Help Me ! » Find A U B » 2024-09-07 12:44:30

harpazo65
Replies: 2

The union of set A with set B, denoted A U B, is the set consisting of elements that belong to either set A or set B, or both.


Given set A = {red, blue, green, white}, and Set B = {red, white, orange, pink}, find A U B.

A U B = {red, blue, green, white} U {red, white, orange, pink}

A U B = {red, blue, green, white, orange, pink}

Is this done correctly?

#48 Re: Exercises » How can i learn math? » 2024-09-07 09:31:35

harpazo65
Irene wrote:

Okay, i will do that.

I can help you with high school algebra.

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