Set A has m elements and set B has n elements. If the total number of subsets of A is 192 more than the total number of subsets of B then the value of m+n is _____.

The number of subsets of a set with 'p' elements is 2^p.

Given that set A has 'm' elements and set B has 'n' elements, the total number of subsets of A is 2^m and the total number of subsets of B is 2^n.

According to the problem, the total number of subsets of A is 192 more than the total number of subsets of B. This can be written as:

2^m = 2^n + 192

We can rewrite 192 as 2^7 * 3, so the equation becomes:

2^m = 2^n + 2^7 * 3

Since the bases are the same, we can equate the exponents:

m = n + 7 * 3

m = n + 21

The problem asks for the value of m + n. Substituting the value of m from the equation above:

m + n = (n + 21) + n = 2n + 21

Without the values of m and n, we cannot find a numerical solution for m + n. However, we know that m + n = 2n + 21.