1.

Two finite sets have m and n elements. The total number of subsets of first set is 56 more than the total number of subsets of the second set. Find the value of m and n.

Answer»

Let A and B be two sets having m and n numbers of elements respectively. 

Number of subsets of A = 2m  

Number of subsets of B = 2n 

According to questions, 

2m - 2n = 56 = × 7 

2n (2m - n - 1) = 23 (23 − 1) 

Therefore, = 3 and m – n = 3 

∴ m = 6



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