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Foggy

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★No,because the number of elements in A and B can be equal however the values of each element can differ between sets

★Yes, because they have the same number of elements and the values of the elements can have the same value thus A=B

Also cus

♩You're hot then you're cold
You're yes then you're no♪
♫You're in then you're out
You're up then you're down♫

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Yes and no. Yes as A and B can contain the same number of elements. No as A can be elements like {2,7,12} while elements in B I like {3,8,13}.

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Not all the time. It can be yes and it can be no it really depends. On the question and the information presented.

For example, when A and B are two sets, when n(A)=n(B) they could contain the same number of elements in their sets but that does not mean that the elements are the same. When they have the same number of elements in the set that makes them equal elements but they might not have the same element. Take for example,A={30,31,33} and B={40,41,42} they both have the same number of elements and thus are equal sets but that does mean A=B.

Min KAi

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Not necessarily. Although sets A and B have the same number of elements it does not mean that A=B.

Eg: If A{10,20,30,40} and B{20,10,40,30}, n(A)=n(B) and A=B as the elements in the sets are the same(order does not matter). This is called an equal set.

However, if A{10,20,30,40} and B{60,70,80,90}, n(A)=n(B) BUT A≠B because the elements in the sets are different. Although sets A and B in this case have completely different elements in their sets, they have the same amount of elements in their sets which makes them equivalent sets.

-keir

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Although n(A) = n(B), it is not necessary that A = B.

An example is that a possible set B could well be composed of a musician, a doctor and a historian, leaving us with:

B = {musician, doctor, historian}

such that n(B) = 3

If another set A pops up comprising of a bat, a rat and Hai Xiang, it would be written as:

A = {bat, rat, Hai Xiang}

such that n(A) = 3

Through thorough thinking and time-consuming things, I have discovered that n(A) = n(B). However, by conceiving careful calculations upon this conclusion, I have escaped my crummy conundrum and now am enlightened to figure out that A does not equal to B. To sum up all my intellectually superior calculations, it is basically that set A and set B do not have the same elements.

This tells me that different sets may hold the same amount of elements, but they are only equal if they contain the same amount of the same elements.

Happy Easter*.

-Arif

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Based on my newly found knowledge on Set Language and especially under the sub topic , Set Equality, for a set to be equal, the number of elements and lists of elements have to be the same.

Both n(A) and n(B) are equal thus making the criterion of same number of elements fulfilled. Making it half way through the same set journey.

But however, in terms of lists of elements, the information provided was too vague and thus impossible to find out because I may have groceries in one bucket and toiletries in the other.

Therefore, I dare not say A=B

: )

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The answer is variable. It could be both yes and no. This is due to the lack of information in the question. The question does not state what are the elements in their respective sets and only that the number of elements are the same.

For example: Lets assume that A{1,3,5,8} and B{8,5,3,1}. These sets will qualify that n(A)=n(B) and that A=B.

However if A{1,3,5,8} and B{2,4,6,9}, then the sets will still qualify for n(A)=n(B), but A=B.

Hence, the sum of the number of elements in the set can never prove that the elements in the sets are the same.

-Matthew

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The answer is dependent on the information that may be missing. since it is only said that :

If A and B are two sets such that n(A) = n(B),

there is a possibility that both set A and B could be equal Sets containing the same elements or that it may just so happen to have the same number of elements it has

For example :

If: A {1,2,3,4} and B {4,3,2,1}, Both Set A and Set B is equal. Thus A=B

However, if : A {1,2,3,4} and B {5,6,7,8}, Then A does not equal to B.

As such, the results on whether A=B or not is totally dependent of the missing information on the elements of both sets A and B consists of .

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It can be yes and no. It is possible that A=B if the elements compromise are similar. It is not possible that A=B if the the sets have different elements but have the same no.

Eg. A(2,3) and B=(3,2), this makes A=B

A(1,2) and B=(3,4), this does not make A=B

Curtis

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It can be both yes and no.

If yes because they both could have the same element thus equal no. of elements.

No because each set could have different elements but have the same no. such as A could be A=(1,3,5) while B is B=(2,4,6). They both have different elements but have the same no. of elements. It's like schrodinger cat

-Abdillah

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Err....It can either be yes or no. Firstly the question is tooooo vague. Furthermore, we do not know what elements do A and B contain. The only thing we know is that the number of elements each sets contain are da same. Thus we still cannot determine whether dem two sets are the same ie. A=B. Therefore this question is not a good question i guess?.

But if the list of elements r da same then of course A=B lah.

(eg. A{1,2,3,4,5} B{1,2,3,4,5}) [A=B]

If they r not the same but still contain the same number of elements then A does not = B lahhhhh.

(eg. A{1,3,5,7,9} B{2,4,6,8,10} ) [A does not = B]

~Joshua Lam here!!!

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It is possible if the elements within comprise of the exact same. However they did not specify and hence the elements might not be exactly same in both sets.

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It's possible that A = B, however, you would need to know which elements are inside both A and B. It is also possible that A ≠ B as n(x) represents the number of elements, not the specific elements themselves.

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Joshua lee, your comment is not counted..

Long ju, are you sure your elements for set B is correct..the one where you stated that x takes value more than 1 but less than 13..

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Yes and No because the number of elements in the sets are the same but the type of element might not be exactly similar. Varun

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they might/might not be equal.

equal, because each of these 2 sets A and B might contain the same no of elements. A( 2,3) B(3,2). both contain the same no of elements regardless of their arrangement. hence, A=B

not equal, because sets A and B might contain diff no of elements. A(3,4) B(2,1). both of them do not have a common element. hence, A isnt equal to B

merry christmas everyone

- jiarong

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It can be Yes and No because. Yes because set A and set B has the same number of elements. No because the number of elements in each set may be different ;)

jerome

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Maybe. 2 sets are equal when they contain the exact same number and type of elements. However, in this case, there is insufficient information to determine is the sets are equal or disjoint. This is so as the question only stated that the number of elements in A is equal to the number of elements in B.

n(A)=n(B)

Thus is it unknown if the elements are exactly the same or different.

Okay, let's say that the sets are equal. Hence, A=B

An example would be:

A={x:x is a number that is >0 but is < 13}

B={x:x is a number that is >1 but is < 13}

Thus:

A={1,2,3,4,5,6,7,8,9,10,11,12}

B={1,2,3,4,5,6,7,8,9,10,11,12}

And so, A=B as they both contain the exact same same and type of elements.

However if the elements are different( since it is already stated in the question that both An and B have the same number of element) A≠B

An example would be:

A={x:x is an odd number <13}

B={x:x is an even number < 13}

Thus:

A={1,3,5,7,9,11}

B={2,4,6,8,10,12}

And so, A≠B as they both contain the same number of elements but not the exact elements.

Hence due to the vagueness of the question, it cannot be assumed that A=B even though both sets have the same number of elements as the requirements are that : For sets to be equal, they must both contain the exact same number and type of elements. Thus because the type of elements in both sets were not stated, it is possible that Set A and Set B could be equal, but at the same time they maybe equal.

龍且(Tan Long Ju)



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多分。彼らは要素の正確な同じ数と種類が含まれている場合2セットは同じです。しかし、この場合には、決定するのに十分な情報がセットが等しいか、互いに素であるが存在します。質問だけAの要素数​​がBの要素の数に等しいことを述べたように、これはそうです
N（A）= N（B）
要素が全く同じであっても異なっていた場合にこのように、未知です。
さて、集合が等しいこととしましょう​​。したがって、A = B
例は次のようになります。
A = {X：X> 0であるが、ある数<13です}
B = {X：xが> 1である数であるが、ある<13}
このように：
A = {1,2,3,4,5,6,7,8,9,10,11,12}
B = {1,2,3,4,5,6,7,8,9,10,11,12}
 だから、どちらもまったく同じ同じで、要素の型が含まれているとして、A = B。
しかし、A≠B（まだアンとBの両方が同じ数の要素を持つことを問題に記載されているため）の要素が異なる場合
例は次のようになります。
A = {X：xが奇数である<13}
B = {X：xが偶数<13です}
このように：
A = {1,3,5,7,9,11-}
B = {2,4,6,8,10,12}
だから、彼らは両方の要素ではなく、正確に同じ数の要素が含まれているとして≠B。
セットが等しくなるようにするために、彼らは両方とも正確に同じ数と種類のが含まれている必要があります。したがってによる質問の曖昧には、A = Bが両方のセットが要件と同じ数の要素を持っていることであっても、と仮定することができません要素。両方のセット内の要素の型が記載されていなかったのでこのように、セットAとセットBが等しいが、同時に彼らは多分等しくなる可能性があります。

龍且(Tan Long Ju)

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If n(A)=n(b), A and B may be different numbers. However, it shows the same number of elements. Therefore, A may not be equal to B.

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Yes and no. n(A) is equal to n(B) but it does not necessarily mean that A and B is the same. And example will be as follow : A= {2,4,6} while B= {1,3,5}. The number of elements is the same but the elements within each set is different

Luqman-kun

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Yes and no. Since n(A)=(B) means they have the same number of elements. However, A and B may be two different sets of items, for example, A={2,4,6 }, while, B={1,3,5}. The number of elements is the same,3, but the elements within each set are different.

-Dylan Tan

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If n(A)=n(B), then A=B. This is because equal sets are sets that contain exactly the same elements. For example, A=(4,5,6,7) and B=(6,5,4,7), then A=B.

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Yes and no as the contents in set A and B may or may not be the same. This only shows that set A and set B have the same number of elements.

Isyraf Khan

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n(A) = n(B) means that both sets have the same NUMBER of elements, not the SAME elements. Thus, A might not be equal to B. 

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n(A) = n(B) means that both sets have the same NUMBER of elements, not the SAME elements. Thus, A might not be equal to B. 

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Kiven Singh

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No. The sum of the number of elements in A is equal to B it may not mean that the elements are the same. For e.g. if A{1,2,3} and B{4,5,6}, the sum of the elements is 3 but the elements are different. Hence, the sum of elements being the same does not mean the elements are the same for both sets.

-Jalen Goh

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Possibly.

First, assuming that the elements of A and B are numbers, we cannot assume that simply because n(A) = n(B) therefore A = B

An example would be to say
A={x : x is the first 3 prime numbers}
B={x : x is the first 3 even numbers}

A = {2,3,5} while B ={2,4,6}

We can say that for this case, A ≠ B.

However, there are of course some exceptions.

An example would be to say
A = {x : first 3 prime numbers}
B = {x : numbers of the Fibonacci Sequence, 1<x<6}

A = {2,3,5} while B = {2,3,5}

In this case A = B

However, this is just looking at numerical numbers. We should not limit math to the constraints of numbers, constants, and calculations. If we include elements of the artistic, abstract or creative nature, then it is harder to safely prove the hypothesis is correct.

For example,
A= {x : majors scales that contain sharps}
B ={x : major scales that contain flats}

A = {G, D, A, E, B, F#, C#} while B = { F, Bb, Eb, Ab, Db, Gb,Cb}
Obviously, A≠B

However, we still cannot prove that A≠B, because there will be exceptions.

A ={the colour of most leaves}
B = {My favourite colour}
A = B

I think the most important argument is an argument of science : correlation does not imply causation.

Just because the colour of most leaves is green and my favourite colour is green, it does not mean that the colour of most leaves changes when my favourite colour does, or vice versa. It's more likely due to the fact that I find green to be a vibrant colour and that leaves contain chlorophyll. This is a huge coincidence.

As such, we cannot say that when n(A) = n(B), A = B, as the amount of elements in each set is superficial and is only equal due to a coincidence.

Perhaps the biggest problem of all is the wording of the hypothesis itself. The question has never stated the chances of A=B, i.e. It has never said 'A can equal B', 'A will equal B' etc. As such, until the hypothesis makes perfect sense, the accuracy of the hypothesis can never be justified properly.

Hai Xiang

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It can be yes and no cos the elements can be the same or different because only the number of elements are the same. The elements can be the same or different.

Muhd Sharizat

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No. Only the number of elements in A=number of elements in B. Contents may not be the same.

-Jøəł Çhęřñ

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In the case where it will be a 'yes', would be when the two given sets are given as 'equal sets'. When that happens, the sets will contain exactly the same elements and hence, it can be said that A=B, because they contain elements that can be found in each other.

i would like to correct a mistake in Zhong Ming's response, that an equal set occurs when both sets contain 'exactly the same elements', and not 'the same number of elements' as claimed, misunderstanding its meaning. Because when he say that, there is a contradiction in his example as despite him proving in his example that the sets are 'disjoint' due to nothing being common, it can be argued that they are 'equal sets' because both has same number of elements, as stated by him.

Donovan Singh

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No this just shows that they have the same number of elements, equal sets. An example is when comparing gender in a class, A{Jane, Mary, Shane} and B{John, Harry,Tom}, they have equal no. of elements but none of the elements have anything in common. Thus they are disjoint sets and not equal

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No this just shows that they have the same number of elements, equal sets. An example is when comparing gender in a class, A{Jane, Mary, Shane} and B{John, Harry,Tom}, they have equal no. of elements but none of the elements have anything in common. Thus they are disjoint sets and not equal

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Zhong Ming