If $n\left(A\right)=43, n\left(B\right)=51\quad and \quad n\left(A\cup B\right)=75, then\quad n\left(A-B\right)\cup\left(B-A\right)$ is equal to
- $53$
- $45$
- $56$
- $66$
The Correct Option is C
Solution and Explanation
Given, \(n(A)=43, \,n(B)=51\) and \(n(A \cup B)=75\)
Now, by addition theorem of probability,
\(n(A \cap B) =n(A)+n(B)-n(A \cup B)\)
\(=43+51-75=19\)
Now, \(n[(A-B) \cup(B-A)]\)
\(=n(A \cup B)-n(A \cap B)\)
\(=75-19\)
\(=56\)
So, the correct option is (C): \(56\)
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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 "|".