First slide

Introduction to sets

Question

Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is

Moderate

Solution

$\begin{array}{l} Given n (A) = m and n (B) = n \\ (Number of subsets of A) - (Number of subsets of B) = 112 \\ \Rightarrow (2^{m}) - (2^{n}) = 112 = (2^{7}) - (2^{4}) \\ ∵ m = 7 and n = 4 \Rightarrow m \cdot n = 28 \end{array}$

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