Question

Помогите упросить. Мат. Логика

Answer 1

$\displaystyle (x\to y)\land(y\to z)\to(x\to z) \\ \\ (x\to y)(y\to z)\to(x\to z) \\ \\ \overline{(x\to y)(y\to z)}+(x\to z) \\ \\ \overline{(x\to y)}+\overline{(y\to z)}+(\overline x+z) \\ \\ \overline{(\overline x+y)}+\overline{(\overline y+z)}+\overline x+z \\ \\ x\overline y+y\overline z+\overline x+z \\ \\ (\overline x+\overline yx)+(z+y\overline z) \\ \\ (\overline x+\overline y)+(z+y) \\ \\ \overline x+z+(y+\overline y) \\ \\ \overline x+z+1 \\ \\ 1$