Question

If $ n(P) = 25 $ & $ n(P \cap Q) = 5 $ then the value of $ n(P - Q) $ is.
a. 10
b. 15
c. 20
d. 25

Answer 1

Hint: Here the question is related to sets where P and Q are the well-defined sets. $ n(P) $ represents the number of elements that set P contains. Here the number of elements of set P and the number of elements contained in both P and Q are given. Now we have to find the number of elements contained only in set P.

Complete step-by-step answer:
Consider two sets namely P and Q and these sets are non-empty sets. The number of elements contained in the set is represented as $ n(set) $ . Here in this question $ n(P) = 25 $ is given. This signifies that 25 elements are contained in the set P. $ n(P \cap Q) = 5 $ signifies that 5 elements are contained in both sets P and Q. Now we have to find $ n(P - Q) $ that is we have to find the elements which contain only in the set P.
To obtain $ n(P - Q) $ we use the formula that is
$ n(P) = n(P - Q) + n(P \cap Q) $ , where the number of elements of set P is represented as the sum of the number of elements contained in the set P and the number of elements contained . We alter the above formula and we rewrite as
$ n(P - Q) = n(P) - n(P \cap Q) $
Substituting the given data, we have
 $ \Rightarrow n(P - Q) = 25 - 5 $
On simplifying we have
 $ \Rightarrow n(P - Q) = 20 $
Therefore 20 elements contained only in the set P.
So, the correct answer is “Option C”.

Note: The question is related to the practical problems related to intersection and union where we use the formulas to find the number of elements the set has contained. By drawing the Venn diagram, we can also obtain the result. Candidate must know the difference of n(P) and n(P-Q)