For any two sets A and B, if n(A) = 15, n(B) = 12, A∩B = Φ and B⊄A, then the maximum and minimum possible values of n(A∆B) are………..and………….respectively.
Solution
Given,
\[ A \cap B = \Phi \]
Therefore,
\[ A \Delta B = A \cup B \]
Hence,
\[ n(A \Delta B)=n(A)+n(B) \]
\[ =15+12 \]
\[ =27 \]
Since the sets are disjoint, the value is fixed.
Therefore,
\[ \text{Maximum value} = 27 \]
\[ \text{Minimum value} = 27 \]
Answer
\[ \boxed{27 \text{ and } 27} \]