#### Answer

The number of subsets = 7

#### Work Step by Step

{X | X is a month that begins with letter 'J' }
We know that only months January, June, July are the months that begins with J.
So, the set = {January, June, July}, which contains 3 elements.
We know that, If set contains n elements then number of subsets are 2^{n}, and among them 2^{n} - 1 are the proper subsets.
Therefore the number of subsets = 2^{3} - 1 = 8 - 1 = 7.