For a binary half-subtractor having two inputs A and B, the correct set of logical expression for the outputs D (= A minus B) and X = borrow) are

A

$$D=AB+ \overline{A} B, X = \overline{A}B$$

B

$$D = \overline{A} B + A \overline{B}, X =  A \overline{B}$$

C

$$D = \overline{A}B + A \overline{B}, X = \overline{A}B$$

D

$$D = AB + \overline{A}B, X = \overline{A}B$$