The ripple counter shown in the figure works as a

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

The minimized form of the logical expression ($$\overline A \,\overline B \,\overline C + B\overline C + \overline A B\overline C + \overline A BC + AB\overline C )$$

The Logical expression $$Y = A + \overline A B$$ is equivalent to