A, b and c are integers. if b is greater than a, then the sum of a and b will always produce a solution c with the same sign as b. true or false?

This would be false because it will depend on the actual values of both a and b, including if they are positive or negative.

This is true.

For example :

B = -6
A = -9

A + B = C = -6 + -9 = -15.

The value is C has the same sign as B.

B = 2
A = -5

A + B = -5 + 2 = -3.

Here The sign for C does not match the sign for B, which is positive.