If A={1,2,3,4,5} and B={} What is AUB?Is B subset A?
Answers
Answer:
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.
A union B = {1,2,3,4 5}
yes B is subset of A .