Math, asked by Priyanka613, 8 months ago

If A and B are two disjoint sets such that n(A)=24 ,n(B)=22.find n(AuB) and n(A-B)

Answers

Answered by lovewithsomeone
0

Answer:If set A = {1,2,3,4} & set B = {4,5,6}, then what is set A-set B?

Originally Answered: If set A = {1,2,3,4} & set B = {4,5,6}, then what is set A-set B?

Others have quite adequately answered the question, but I'd like to add to it.

Let A and B be two sets.

Steps to perform operation  A−B .

1. Look at each element of A one-by-one. See if it is present in B or not. If it is present in B, mark it (in set A).

2. Now, remove all the elements of set A that you have marked in above step. The remaining set is your answer.

So, for the example asked proceed as follows.

Start with the first element of set A i.e. "1". Is it in set B? No.

Go to the next element of set A ("2"). Is it in set B? No.

Go to the next element of set A ("3"). Is it in set B? No.

Go to the next element of set A ("4"). Is it in set B? Yes. Mark it in set A.

Now, remove all marked elements of set A. There was only one, i.e. "4".

The remaining set is {1, 2, 3}. This is the answer for A-B.

NOTE:  A−B≠B−A .

To perform B-A, do the "opposite". Look at each element of set B and see if it occurs in set A or not. If it occurs in set A, mark it (in set B). Now, simply remove the elements that you have marked in set B. The remaining set if your answer.

So, for the example asked proceed as follows.

Start with the first element of set B i.e. "4". Is it in set A? Yes. Mark it.

Go to the next element of set B ("5"). Is it in set A? No.

Go to the next element of set B ("6"). Is it in set A? No.

Now, remove all marked elements of set B. There was only one, i.e. "4".

The remaining set is {5, 6}. This is the answer for B-A.

A more general method to go from A-B to B-A or vice-versa.

In the first step of marking the common elements, mark them in both the sets. It doesn't take extra effort as you are comparing once anyways.

Now, to get A-B, simply remove the marked elements of set A, while to get B-A simply remove the marked elements of set B.

In mathematical terms,

A−B=A−(A∩B)  

B−A=B−(B∩A)  

Note that,  (A∩B)=(B∩A)  that is, you need not check the common terms of A and B twice. Simply check them starting with either A or B and the other one too will be taken care of (it's pretty obvious if you think about it).

The symbol  ∩  denotes "intersection", i.e. the set of all common elements of A and B.

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Answered July 28, 2018 · Author has 471 answers and 1M answer views

If A and B are disjoint set then what is n(A-B)?

Since A and B are disjoint sets, there are no common elements among A and B i.e., set intersection is empty.

In set difference, we exclude the common elements among both the sets and write the remaining elements of the first set.

Here, there are no common elements and we should write the first set elements as it is.

Therefore,

A−B=A, if A and B are disjoint  

⟹n(A−B)=n(A)  

In other words, the cardinality of set difference can be expressed as:

n(A−B)=n(A)−n(A∩B)  

[∵We exclude common elements  

and write the rest of the first set  

Answered by abhi178
3

Given info : If A and B are two disjoint sets such that n(A) = 24 , n(B) = 22.

To find : the value of n(A U B) and n(A - B)

solution : if A and B are two disjoint sets,

A n B = Φ ⇒n(A n B) = 0

now n(A U B) = n(A) + n(B) - n(A n B)

= 24 + 22 - 0

= 46

Therefore the value of n(A U B) = 46.

n(A - B) = n(A) - n(A n B)

= 24 - 0

= 24

Therefore the value of n(A - B) = 24.

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