Question:
If $n(\mu) = 48 , n(A) = 28, n(B) = 33$ and $n(B - A) = 12$, then $n(A \cap B)^C$ is
If $n(\mu) = 48 , n(A) = 28, n(B) = 33$ and $n(B - A) = 12$, then $n(A \cap B)^C$ is
Updated On: Jul 6, 2022
- 27
- 28
- 29
- 30
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The Correct Option is A
Solution and Explanation
$n\left(\mu\right) =48 , n\left(A\right)=28 , n\left(B\right)=33$
$ n\left(B-A\right) =12 $
$n\left(A \cap B\right) =n\left(B\right) -n\left(B -A\right) =33 -12 =21$
$ n\left(A \cap B\right)^{C} = n\left(\mu\right) -n=\left(A\cap B\right)=48 -21 =27 $
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".