Multiple choice

Consider the Boolean function f(w, x, y, z). Suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i1 = < w1, x1, y1, z1 > and i2 = < w2, x2, y2, z2 >, we would like the function to remain true as the input changes from i1 to i2 (i1 and i2 differ in exactly one bit position), without becoming false momentarily. Let $f(w, x, y, z) = \sum(5, 7, 11, 12, 13, 15)$. Which of the following cube covers of f will ensure that the required property is satisfied?

  1. $\bar wxy, wx\bar y, x\bar yz, xyz, wyz$
  2. $wxy,\bar wxz, wyz$
  3. $wx,\overline {yx} xz, w\bar xyz$
  4. $wzy, wyz, wxz, \bar wxz, x\bar yz, xyz$
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