Let $A$ and $B$ be two sets such that$n\left( A \right) = 20,n\left( {A \cup B} \right) = 42$ and $n\left( {A \cap B} \right) = 4$:
Find $n\left( {B - A} \right)$.
Answer
364.2k+ views
Hint: In this question we have been given with two sets A and B and the values of some set operations are given, using these values we are supposed to find the number of elements that are in B but not in A, we can simply use the formula of intersection to obtain the elements in set B and then subtracting that with the intersection will give us the answer.
Note: While solving these questions, it is very important to apply the correct formula to obtain the answer. In this question, we used the formula of intersection first to obtain the elements in B and then subtracted with the intersection to get the answer.
Complete step by step answer:
It is already given that,
$n\left( A \right) = 20$,
$n\left( {A \cup B} \right) = 42$
And,
$n\left( {A \cap B} \right) = 4$
Using the formula,
$n\left( B \right) = n\left( {A \cup B} \right) + n\left( {A \cap B} \right) - n\left( A \right)$
Therefore, on putting the values in the formula, we get,
$n\left( B \right) = 42 + 4 - 20$
$n\left( B \right) = 26$
$n\left( {B - A} \right) = n\left( B \right) - n\left( {A \cap B} \right)$
$n\left( {B - A} \right) = 26 - 4$
$n\left( {B - A} \right) = 22$
It is already given that,
$n\left( A \right) = 20$,
$n\left( {A \cup B} \right) = 42$
And,
$n\left( {A \cap B} \right) = 4$
Using the formula,
$n\left( B \right) = n\left( {A \cup B} \right) + n\left( {A \cap B} \right) - n\left( A \right)$
Therefore, on putting the values in the formula, we get,
$n\left( B \right) = 42 + 4 - 20$
$n\left( B \right) = 26$
$n\left( {B - A} \right) = n\left( B \right) - n\left( {A \cap B} \right)$
$n\left( {B - A} \right) = 26 - 4$
$n\left( {B - A} \right) = 22$
Note: While solving these questions, it is very important to apply the correct formula to obtain the answer. In this question, we used the formula of intersection first to obtain the elements in B and then subtracted with the intersection to get the answer.
Last updated date: 30th Sep 2023
•
Total views: 364.2k
•
Views today: 8.64k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE
