Question:
Let $n(A - B) = 25 + x, n (B -A)= 2x$ and $n(A \cap B) = 2x$. If $n(A) = 2 (n(B)) $ then 'x' is
Let $n(A - B) = 25 + x, n (B -A)= 2x$ and $n(A \cap B) = 2x$. If $n(A) = 2 (n(B)) $ then 'x' is
Updated On: Jul 6, 2022
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The Correct Option is B
Solution and Explanation
$n\left(A -B\right)= 25 +x, n\left(B-A\right) =2x$
$ n\left(A \cap B\right) =2x $
$n\left(A\right) =n\left(A -B\right) + n\left(A\cap B\right) $
$= 25+x+2x=25 +3x $
$n\left(B\right)=n \left(B-A\right)+n \left(A\cap B\right)=2x+2x=4x$
$n \left(A\right)=2n \left(B\right)\Rightarrow25+3x=2\left(4 x\right)$
$\Rightarrow 5x=25 \Rightarrow x=5$
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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 "|".