The question is:
Let the sets S and T be defined a follows:
S=x:x is a positive integer multiple of 3 less than 100
T=x: x is a positive integer multiple of 4 less than 100
If ℘ (X) represents the power set of X for any any set X, how many elements are there in ℘ (S) ∩ ℘ (T)?
Now if it asked for the intersection of S and T, then the answer would simply be {12, 24, 36, 48, 60, 72, 84, 96}. It is asking for the intersection of two power sets, and there are so many elements in the power sets of both the sets. Is there any shortcut method which can be used? Any help would be appreciated.
Best Answer
The elements in the intersection of power set of both sets will be same as the elements in power set of intersection of both sets.(as hinted by Andrea Mori)
Hence ,answer to your question will be the number of elements in power set of {12,24,36,48,60,72,84,96} i.e 2⁸= 256.
You can verify this by taking any simpler example.
Hope it helps:)