Question

if A and B are two sets such that n(A)=150 n(B) =250 and n(A union B) =300 find n(A-B) n(B-A)

Answer 1

Hey there! Thanks for the question!

This question is from the topic sets. First of all a brief overview, and explanation of the terms used above.

Set is the collection of some objects. A set can have zero elements, finite or infinite elements.

Union of two sets A & B is represented by A ∪ B, The Set Union of A, B is the set of elements that belongs to Either A or B or both.

A - B, The difference between the sets, is the set of elements in A that doesn't belong to B.
B - A is the set of elements that belongs to B but not A.

So, In the given question

A and B are two sets such that,
n ( A) = 150
n ( B) = 250

We are also given the value of A ∪ B.

So, Let's look at the formulae we have

$n ( A \bigcup B ) = n ( A) + n ( B) - n ( A \bigcap B ) \: \:$

So , We will find value of n ( A∩B ) now,

$300 = 150 + 250 - (A \bigcap B) \\400 - 300 = (A\bigcapB) \\ (A\bigcapB) = 100$
Now,

Let's look at one more formula,

$n ( A \bigcup B) = n ( A - B)+ n( B) \\ 300 = n ( A - B) + 250 \\ 300 - 250 = n ( A - B) \\ 50 = n ( A - B)$

$n ( A \bigcup B) = n ( A )+ n( B -A) \\ 300 = 150 + n( B -A) \\ 150 = n( B -A)$

We have found that,
n ( A - B) = 50
n ( B - A) = 150 .

How do we know if we are correct, We do have a formula to check,

That is,

$n( A \bigcup B) = n ( A - B ) + n ( B - A) + n(A \bigcap B )$

Substituting the values,
$300 = 50 + 150 + 100 \\ 300 = 300$

We see both L. H. S and R. H. S are equal, Hence our solution is correct.

$\boxed{ Therefore, \: n ( A - B) = 50 , \: n ( B - A) = 150 }$

Answer 2

$\huge \bf{hey}$

$\huge \underline{here \: is \: the \: answer}$
⤵⏬⬇

$\bf{this \: refers \: to \: the \: pic}$
$\huge{hope \: it \: helps}$
$\huge \color{red}{thanks}$