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

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 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

2m-2n=112 m=7, n=4 (27-24=112) m × n=7 × 4=28

Q. 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 $m \cdot n$ is

$2^{m} - 2^{n} = 112$
$m = 7, n = 4$
$(2^{7} - 2^{4} = 112)$
$m \times n = 7 \times 4 = 28$

Q. 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

2m−2n=112 m=7,n=4 (27−24=112) m×n=7×4=28

Q. 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 $m \cdot n$ is

$2^{m} - 2^{n} = 112$
$m = 7, n = 4$
$(2^{7} - 2^{4} = 112)$
$m \times n = 7 \times 4 = 28$