Olympiad workbookIOQMSets and Relations
Let A and B be two finite sets such that there are exactly 144 sets which are subsets of A or subsets of B . Find the number of elements in A B .
Correct answer
08
Step-by-step solution
aligned & 2^ a+b +2^ b+c -2^b=144=2^4 9 & 2^b (2^a+2^c-1 )=2^4 9 & b=4 & a=1, c=3 & n(A B)=5+7-4=8 aligned