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$A$ and $B$ are two sets such that $n(A) * n(B) = 7$ and  $A \subset K \subset B$, where $n(X)$ is the cardinality of set $X$ and $K$ is a set. Then, to satisfy proper subset constraint, the total number of  $K$ sets possible is _______.
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We can assume $A = \{a\}$ and $B = \{a,b,c,d,e,f,g\}$ such that $n(A) * n(B) = 7$

Now $a \in K$.

$B \backslash A = \{b,c,d,e,f,g\}$ , here $2^6$ subsets are possible. Now $K$ must include elements from one of such $2^6$ subsets but it can not be $\phi$ nor $B \backslash A$. 

There total no of possible $K$'s $= 64 - 2 = 62$

Total number of possible set is : 26 - 2 = 62

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