Suppose that we have a 4-bit input integer x, represented by four Boolean variables {x0, x1, x2, x3} as in Exercises 3.29–3.32. Let y be the integer x + 1, represented again as a 4-bit value {y0, y1,...

Suppose that we have a 4-bit input integer x, represented by four Boolean variables {x₀,
_x1,
x₂, x₃} as in Exercises 3.29–3.32. Let y be the integer x + 1, represented again as a 4-bit value {y0, y1, y2, y3}. (For the purposes of this question, treat 15 + 1 = 0—that is, we’re really defining y = (x + 1) mod 16.) For example, for x = 11 (which is 1011 in binary), we have that y = 12 (which is 1100 in binary). For each i ∈ {0, 1, 2, 3}, give a proposition over the Boolean variables {x0, x1, x2, x3} that expresses the value of yi .