## Question

A is a set containing *n* elements. A subset *P* of *A* is chosen. The set *A* is reconstructed by replacing the elements of *P*. A subset *Q* of *A* is again chosen. The number of ways of choosing *P* and *Q* so that P ∩ Q = Ï• is

### Solution

For *a _{i}* ∈

*A*, we have the following choice:

Out of these only (ii), (iii) and (iv) imply .

Therefore, the number of required subset is 3* ^{n}*.

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