Let A,B, and C be sets.?

Prove that A is a subset of B iff A-B= empty set.

Let A,B, and C be sets.?
Let "n" denote intersection, "u" denote union, and B' be the complement of B. By definition, A-B = A n B'





1. Proving =%26gt;


Start with letting A be a subset of B.


Let's try using proof by contradiction here.


Suppose that A-B is nonempty.


Then there exisits an element x such that x is in A-B.


That means that x is in A n B'.


That means that x is in A and x is in B'


Since x is in A, and A is a subset of B, then x is in B.


This is a contradiction, because x cannot be in both B and B'.


So that must mean that A-B = empty set.





2. Proving %26lt;=


Now suppose that A-B = A n B' = empty set.


Let x be in A.


Then x is in (A n B) u (A n B') since A = (A n B) u (A n B').


Then either x is in (A n B) or x is in (A n B').


However x cannot be in A n B' since it is the empty set.


So that must mean that x is in A n B.


Which means that x is in B.


That means that A is a subset of B.
Reply:A-B is well known as A n B'. You should know that, Dr. D. Report It

Reply:A is a subset of B if


A intersect B = A





AunionB = A + B - AintersectB


If A is a subset of B, then


AunionB = B





I'm not sure what your term A-B means.

Suppose A, B, C are sets and consider the function?

(or mappings) f: A -%26gt; B and g: B -%26gt; C.


i. show that if f and g are both injective then so is their composition g*f


ii. show that if f and g are surjective then so is their composition g*f


recall that (g*f)(a)=g(f(a))

Suppose A, B, C are sets and consider the function?
(i) if f and g are injective then f(a) = f(b) iff a=b and g(c) = g(d) iff c=d


hence g(f(a)) = g(f(b)) iff f(a) = f(b) iff a=b





so g*f is injective





(ii) f and g are surjective iff for all b in B there exists a in A such that f(a)=b and similarly the exists b in B such that g(b) = c for all c in C


so for all c in C there exists b in B such that g(b)=c, and for all b in B there exists a in A such that f(a) = b


therefore, for all c in C there exists a in A such that g(f(a)) = c, and g*f is surjective





and as g*f is both surjective and injective it is also bijective!

Can anyone find (A - B) - C and A - (B - C). Are these sets equal?

Can anyone find (A - B) - C and A - (B - C). Are these sets equal?

Can anyone find (A - B) - C and A - (B - C). Are these sets equal?
These are not congruent.





Consider the distributive property...


(A - B) - C = A - B - C


A - (B - C) = A - B + C





I'm trying to think of an example of sets... but I am wondering what your context is... what are you working on?





In an elementary mathematics situation...


consider A = 10, B = 5 and C = 2


(A - B) - C = (10 - 5) - 2 = 5 - 2 = 3


and


A - B - C = 10 - 5 - 2 = 5 - 2 = 3





A - (B - C) = 10 - (5 - 2) = 10 - 3 = 7


and


A - B + C = 10 - 5 + 2 = 5 + 2 = 7





I'm not sure if this helps, if can elaborate on the context I might be able to shed more light onto the subject... :-)
Reply:No, they are not equal. It is an order of operations problem.
Reply:No , because The associative property of real numbers which means ( Changing the grouping does not affect the result ) is not applied on subtraction


Just addition and Multiplication
Reply:Let m be an element of Sets A and C, but not of set B.





Then m cannot belong to (A-B)-C:


m belongs to A and m does not belong to B, means that m belongs to (A-B). However, because m also belongs to C, it is removed when performing the -C operation.





However, m belongs to A - (B-C):





m belongs to C but not to B, therefore, m does not belong to (B-C).


m belongs to A and it is not removed when performing the - (B-C) operation.





Therefore:


m belongs to A - (B - C),


but


m does not belong to (A - B) - C





-----





Let A be the set of all positive integers from 1 to 9


Let B be the odd subset of A.


Let C be the even subset of A.


Let m=2 (or any other even element of A)





A={1, 2, 3, 4, 5, 6, 7, 8, 9}


B={1, 3, 5, 7, 9}


C={2, 4, 6, 8}





(A-B) = {2, 4, 6, 8}


(A-B)-C = {2, 4, 6, 8} - {2, 4, 6, 8} = empty set


(m does not belong to the empty set)





(B-C) = {1, 3, 5, 7, 9}


because no elements of C are contained in B, subtracting C from B has no effect on B; (B-C) = B


A-(B-C) = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 3, 5, 7, 9} =


A-(B-C) = {2, 4, 6, 8} = C


C is not equal to the empty set


(m belongs to C)
Reply:A-B = A%26amp;B'


(A-B)-C = (A%26amp;B')-C=(A%26amp;B')%26amp;C' = A%26amp;B'%26amp;C'





A-(B-C) = A%26amp;(B-C)' = A%26amp;(B%26amp;C')' = A%26amp;(B'||C) = (A%26amp;B'||A%26amp;C)





SO THEY ARE NOT EQUAL
Reply:no they arent.


the parentheses changes everything.





see i will use the nubers 7(a) 6(b) and 5(c) as an example.





(a-b)-c


(7-6)-5


you always have to do parentheses first.


soo 7-6 is 1.


you can take the parentheses away.


1-5= -4





the next one...


a-(b-c)


7-(6-5)


once again...parentheses first.


soo 6-5 is 1.


7-1 is 6.





see? perentheses does count.


the first one was -4 and the second one was 6.





hope this helped.


sometimes when i explain math, no one gets me.
Reply:No, they're not equal


Say A is 1, B is 2, C is 3. The first problem would go like this


(1 - 2) - 3. You'd do the problem in the parenthesis first, you'd get -1, then -3 more would be -4.





The second equation, would be


1 - (2 - 3)


Again, parenthesis first.. you'd get -1, then minus the 1 on the outside (A) would be -2. Different answers.
Reply:They are not equal.


when we open (A-B)-C it is A-B-C


but when we open A-(B-C) it is A-B+C


minus sign has to be multiplied with +B AND -C, which are in the bracket, and which will become -B+C.


WANT TUTIONS IN MATHEMATICS, TELL. IT WILL ALL BE FREE FOR TWO HOURS EVERY SATURDAY ON NET.

elephant ear

If A, B, and C are sets, prove that:?

C \ (A and B) = (C \ A) or (C \ B).

If A, B, and C are sets, prove that:?
Just do a mutual inclusion argument.


Say x is in C \ (A and B). Then x isn't in both A and B, and so in particular must not be in one of them (or if you like, in the complement of one of them). Say x is not in A. Then x is in C\A, and so in (C \ A) or (C \ B). Similarly, if x is not in B, then it is in C\B and also (C \ A) or (C \ B).





Now the other way. Say x is in (C \ A) or (C \ B). If x is in C\A, then x must be in C, but cannot be in A. Therefore x is also not in (A and B), and so x is in C\(A and B). Same thing works if x is in C\B.
Reply:uhh you can try substituting numbers in for the letters like 3, 4, 5 and see if they come out equaling each other.
Reply:Those are letters of the alphabet.

If A, B, and C are sets, prove that:?

C \ (A or B) = (C \ A) and (C \ B)

If A, B, and C are sets, prove that:?
That does not look too right. Check it on a Venn diagram.


I'm assuming that or means union;


and means intersection.





C \ (A u B) = C\A u C\B


and C\(AnB) = C\A n C\B

What is cheaper? - Turning off the A/C (air conditioner) or setting it to a higher temperature while gone?

When no one is at home, I set the a/c to "off" and then it turns on about 30-45 minutes before I get home (programmable thermostat). Alternatively, I could set the thermostat to a higher temperature during the day, but I don't want it to run all day even if it is at a higher temperature. However, by turning it off all day, will the a/c consume just as much power when it comes on in the evening to get things cool again? I live in Texas, so summers get really hot! I'm also out of the house for around 10-12 hours during the week. Any advice? Does the opposite hold true in winter???

What is cheaper? - Turning off the A/C (air conditioner) or setting it to a higher temperature while gone?
It is better for you to have it off during the day and come on a short time before you get home. It is harder for your a/c to cycle on and off all day keeping it at 80 something, than to run for 30 min to and hour straight. The same is true with your heater in the winter. The total amount of time the a/c runs is less so it costs less. Use your programmable thermostat how it was designed, don't heat or cool and empty house.
Reply:Unless you have an A/C that is over 15 years old, you should turn it off every time you are gone for more than half an hour. An A/C in good condition should cool off a house in about an hour. A/Cs over 15 years old may not be very efficient and should be turned off.





Leaving the A/C running the whole day only costs you money. Keep in mind that if you have pets, you might consider some sort of way for them to cool off.





If your A/C has a fan only feature, Have it come on after the sun is strongest, so that it will circulate fresh air in the house, and then have the A/C come on 30-45 minutes before you come home.





The same applies for winter except for the fan. There is no need to heat the house if you are not in it.





You'll see a big difference in your utility bill.





Good luck.
Reply:I am also a Texan, so I know how hot summers get. Personally, and I have no firm data to back this up, I leave the thermostat at a higher temperature (usually around 80 degrees during the day) to preserve a moderate level of coolness in the house. I usually run my thermostat at about 70 degrees while I am at home. When I leave for several days, I elevate the temp. to about 85. My bills have been more reasonable running like this rather than shutting it off when I am gone. In winter, I turn the thermostat down to 60 degrees when I leave and then run it at about 68-70 when I get home. Our winters have been pretty mild lately.
Reply:I would raise the temperature when absent. It'll keep the humidity down.





But this isn't easy to provide an all knowing answer. If you have excellent insulation and a pretty tight seal, you could probably save more by shutting it off. But if your home is average, you are just going to have to suck the heat out of the walls, ceilings and furniture if you don't keep some kind of minimal cooling going.





And yes, opposite for winter. Plus in winter you might not want it completely off if your pipes could freeze.





Another aspect is comfort, perhaps more so with heat. Yes, your could drop it down to 55 F when gone. With forced air the room air will heat up quickly. Then the thermostat kicks off. But in mere minutes the cold walls suck in that heat and you will feel chilly. Then the heater kicks on again. In my small office building it takes about an hour for the walls/furniture and floor to reach ambient and for me to feel "comfortable" during the periods the heater is not running.
Reply:I have mine turned down during the day and and night when we are sleeping heat wise and it saves money. but for the A/C i didn't see much change either way in my bill by turning it up as to turning it off so do what you will i leave mine to when its about 75 during the day when no one is home and 68-70 when we are home.
Reply:I was told by the electric company to conserve engery turn off all appliances while your gone. If you can set them to come on like your air conditioner before you get home, do that to cool it down. We have central air so it maintains the houses temp. I do keep it warmed in the daytime since we are not here but at 5pm it starts to cool down. In the winter we alway keep the house cooler than in the evening. The thermostate is programmed at 7am to go to 63 degrees. In the evening at 5pm it goes up to 68.
Reply:I would turn it up. Due to the fact you live in TX. IT will help keep the humidity down. My brother used to turn his off, it got old coming home with kids to a hot house in the Summer time.
Reply:Set your a/c to a higher temp. it will use more energy and is harder on the a/c when it has to kick on and off all the time.
Reply:Set it at a higher temp when you are not home so that the a/c can maintain a comfortable temp and so it won't have to work so hard to drop the temp when you get home. starting a/c equipment when your house is hot creates a big load for it, causing it to consume more energy and possibley more wear and tear in the long run.
Reply:Its cheaper to set it at a higher temp. Talk to your local power company about other energy saving tips.

Why is it that the C-word is the worst thing you can call a woman?

Why does c*nt set of a deep burning rage in most women???

Why is it that the C-word is the worst thing you can call a woman?
its disrespectful and degrading
Reply:I personally just hate the word and think that it sounds trashy when anyone says it... but thats just my opinion :)
Reply:i call women classy all the time i never get any kick back
Reply:that is not the worst thing you can call a woman..people with tiny minds and smaller wieners just think that.
Reply:I think the worst thing you can call a woman is by your ex-girlfriends name.
Reply:Why would a woman care you if called her a cock?





Oh, you're talking about the word ****! I see. Well, is that really worse than calling a woman a *****, pussy-lips, a ***-gargling slut, a pleasure-box, a cock-rider, a dick-licker, a dyke, a filthy, filthy whore, or a moderately unattractive person?
Reply:shut up c#nt
Reply:I've never been called that luckily but it would not really bother me, since it is such a generic word.





I would be affected the most by someone saying that I was worthless.





OUCH!
Reply:I don't know.





All bad words are only bad because someone a long time ago decided they were bad. I mean, what idiot decided the middle finger was so horrible? I just think the whole thing is stupid.
Reply:Because it defines them as being nothing more than their basic identifying sexual organ. The most minimal part of their existance that a man could need to care about. And crudely at that.
Reply:i have no idea i just know it ISNT something you call a girl. i think its like b*tch tiomes 1000000 or something......
Reply:No more than what the I-word should do for you.





YOU IDIOT
Reply:do you like women to call you a pr*ck?????????? same diff...
Reply:Because it reduces us to nothing more than an object put on this Earth solely for a man's sexual pleasure.
Reply:It just has dirty connotations and a dirty sound to it. Like twat does.
Reply:theres loads of word begin with C WHICH ONE ARE YOU ASKING ABOUT
Reply:What is the C-word?
Reply:The word itself isn't what makes a cuss word bad, it's how deeply loaded with hatred it is.
Reply:mmmmmmmm you opened acan of worms





c*nt is they worse thing you could say or b*tch


women dont even call each other c*nts
Reply:lol whats the c-word?


i dont know it


TELL ME!!!
Reply:It is the most degrading and disrepectful name that a woman can be called. All name calling is disrespectful.
Reply:I am not sure.. but the word just sounds vulgar.. Maybe thats why..
Reply:i dont f**king know,is it a woman thing or what ..c**t c**T or what,i like funking cart cart....
Reply:I think because it's very vulgar and is used in a negative connotation... I use it though haha. I think showing you're insulted only proves that you've been bothered by something and the other person has "won"...if someone uses that word I laugh it off and say wow that was weak...they tend to get pissed and leave it at that...

lady palm