Let x1n be a signal that takes nonzero values only between n

Let x_1[n] be a signal that takes non-zero values only between n = 0 and n = M and x_2[n] be a signal that takes non-zero values only between n = 0 and n = L. Consider the convolution x_1[n]* x_2 [n]. For what values are n can you assert that x_1[n]* x_2 [n]is definitely zero.

Solution

The limits of the convolution lies between the sum of lower limits and sum of upper limits of the two signals

From this we can tell that the values less than ZERO (ZERO+ZERO) lower limits and greater than M+L ( SUM OF UPPER LIMITS) should be ZERO