91Ó°ÊÓ

Find the value of the Boolean expressions for $$x_{1}=1, \quad x_{2}=1, \quad x_{3}=0, \quad x_{4}=1$$. \(\overline{x_{1} \wedge x_{2}}\)

Prove or disprove the equations. $$ \overline{\bar{x}}=x $$

Find the value of the Boolean expressions for $$x_{1}=1, \quad x_{2}=1, \quad x_{3}=0, \quad x_{4}=1$$. $$ \left(x_{1} \wedge \bar{x}_{2}\right) \vee\left(x_{1} \vee \bar{x}_{3}\right) $$

Find the disjunctive normal form of each func. tion using algebraic techniques. (We abbreviate \(a \wedge b\) as \(a b .)\) \(f(x, y)=x \vee x y\)

Find the disjunctive normal form of each func. tion using algebraic techniques. (We abbreviate \(a \wedge b\) as \(a b .)\) \(f(x, y)=(x \vee y)(\bar{x} \vee \bar{y})\)

Find the value of the Boolean expressions for $$x_{1}=1, \quad x_{2}=1, \quad x_{3}=0, \quad x_{4}=1$$. $$ x_{1} \vee\left(\bar{x}_{2} \wedge x_{3}\right) $$

Find the disjunctive normal form of each func. tion using algebraic techniques. (We abbreviate \(a \wedge b\) as \(a b .)\) \(f(x, y, z)=x \vee y(x \vee \bar{z})\)

Find the value of the Boolean expressions for $$x_{1}=1, \quad x_{2}=1, \quad x_{3}=0, \quad x_{4}=1$$. $$ \left(x_{1} \wedge\left(x_{2} \vee\left(x_{1} \wedge \bar{x}_{2}\right)\right)\right) \vee\left(\left(x_{1} \wedge \bar{x}_{2}\right) \vee\left(\overline{x_{1} \wedge \bar{x}_{3}}\right)\right) $$

Prove or disprove the equations. $$ \bar{x}_{1} \wedge\left(\left(x_{2} \wedge x_{3}\right) \vee\left(x_{1} \wedge x_{2} \wedge x_{3}\right)\right)=x_{2} \wedge x_{3} $$

Find the disjunctive normal form of each func. tion using algebraic techniques. (We abbreviate \(a \wedge b\) as \(a b .)\) \(f(x, y, z)=(y z \vee x \bar{z})(\overline{x \bar{y} \vee z})\)