Question

Let A and B be two sets such that \[n(A) = 0.16,n(B) = 0.14,n(A \cup B) = 0.25\]. Then \[n(A \cap B)\] is equal to
A.\[0.3\]
B.\[0.5\]
C.\[0.05\]
D.None of these

Answer 1

Hint: Sets are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}.The order of a set defines the number of elements a set is having. It describes the size of a set. The order of sets is also known as the cardinality. We must remember the formula for union of two sets in order to solve the given problem.

Complete step-by-step answer:
Universal set : A universal set is a set which contains all the elements or objects of other sets, including its own elements. It is usually denoted by the symbol ‘U’.
Union of sets: If set A and set B are two sets, then A union B is the set that contains all the elements of set A and set B. It is denoted as \[A \cup B\].
Intersection of sets: If set A and set B are two sets, then A intersection B is the set that contains only the common elements between set A and set B. It is denoted as \[A \cap B\].
Complement of a set: The complement of any set, say A , is the set of all elements in the universal set that are not in set A. It is denoted by \[A'\] .
For any two sets A and B we have :
\[n(A \cup B) = n(A) + n(B) - n(A \cap B)\]
If \[A \cap B = \phi \] then \[n(A \cup B) = n(A) + n(B)\]
Here in this question we have to find the value of \[n(A \cap B)\] .
We are give the values \[n(A) = 0.16,n(B) = 0.14,n(A \cup B) = 0.25\] .
We know that \[n(A \cup B) = n(A) + n(B) - n(A \cap B)\]
Therefore putting the values given we get ,
\[0.25 = 0.16 + 0.14 - n(A \cap B)\]
\[n(A \cap B) = 0.16 + 0.14 - 0.25 = 0.05\]
So, the correct answer is “Option C”.

Note: A universal set is a set which contains all the elements or objects of other sets, including its own elements. The elements in the sets are depicted in either the Statement form, Roster Form or Set Builder Form. Cardinality of a set can never be a negative number.