I am totally guessing at this one.

Let k and n be positive integers satisfying k < n. How many subsets of [n] are not also subsets of [k]?

Take k=2 and n=3, then

[3] = { } {1} {2} {3} {1,2} {1,3} {2,3} {1,2,3}

[2] = { } {1} {2} {1,2}

The cardinality of [3] = and the cardinality of [2] = . The number of subsets of [3] that are not subsets of [2] = - .

So I think the number of subsets of [n] that are not also subsets of [k] would be - . Is this correct?