I have to find out the DNF of $$f(x,y,z)=x\wedge\left(\overline y\vee\overline z\right),$$ being $f$ a function of Boole.
$$\begin{array}{ll} f(x,y,z)&=x\wedge \left(\overline y\vee\overline z\right)\\ &=\left(x\wedge\overline y\right)\vee\left(x\wedge\overline z\right)\\ &=\left(x\wedge\overline y\wedge 1_A\right)\vee\left(x\wedge\overline z\wedge 1_A\right)\\ &=\left(x\wedge\overline y\wedge \left(z\vee\overline z\right)\right)\vee\left(x\wedge\overline z\wedge\left(y\vee\overline y\right)\right)\\ &=\left(x\wedge\overline y\wedge z\right)\vee\left(x\wedge\overline y\wedge\overline z\right)\vee\left(x\wedge\overline z\wedge y\right)\vee\left(x\wedge\overline z\wedge\overline y\right)\\ &=\left(x\wedge\overline y\wedge z\right)\vee\left(x\wedge\overline y\wedge\overline z\right)\vee\left(x\wedge\overline z\wedge y\right), \end{array}$$
being $1_A$ the last element.
Is it right? Thanks!