The number $$43$$ in $$2's$$ complement representation is

The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$ $$$x+y+z=1$$$ $$$xy=0$$$ $$$xz+w=1$$$ $$$xy + \overline z \overline w = 0$$$
have the following for $$x, y, z$$ and $$w,$$ respectively.

Which function does NOT implement the Karnaugh map given below?

A relation R is defined on the set of integers as zRy if f (x + y) is even. Which of the following statements is true?