vipulgoyal wrote:A set of n elements has 2^n subsets, including both the set itself and the empty set. How many common subsets do set {1, 2, 3, 4} and set {2, 3, 4, 5} have?

The common subsets can only have the common elements : 2, 3, and 4.
Hence, number of common subsets = Number of subsets of the set {2, 3, 4} = 2^3 = 8

rintoo22 wrote:which subsets am I missing ?

Subsets containing three elements.
In 1st case : {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, and {2, 3, 4}
In 2nd case : {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, and {3, 4, 5}

I'll take the opportunity to explain why the a set of n elements has 2^n subsets.

To create a subset, we may or may not select each of the n elements.
Hence, for each element, we have 2 options : either include it in the subset or don't.
So, total number of possible subsets = 2*2*2* ... (n times) = 2^n
When none of the elements are included in the subset, we get the null set and when all of the elements are included in the subset, we get the original set itself.

Hope that helps.