Multiple choice

Consider a 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 $ i_{1}=\left \langle w_{1}, x_{1}, y_{1},z_{1}\right \rangle $ and $ i_{2}=\left \langle w_{2}, x_{2}, y_{2},z_{2}\right \rangle $ , we would like the function to remain true as the input changes from $ i_{1}$ to $ i_{2}$ ($ i_{1}$ and $ i_{2}$ 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. $ \overline{w}xz,wx\overline{y},x\overline{y}z,xyz,wyz$
  2. $ wxy, \overline{w}xz,wyz$
  3. $ wx\overline{y} \overline{z}, xz, w\overline{x}yz$
  4. $ wx\overline{y}, wyz, wxz, \overline{w}xz, x\overline{y}z, xyz$
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Explanation