91Ó°ÊÓ

Simplify each boolean expression using the laws of boolean algebra. $$w x y z+w^{\prime} x y^{\prime} z^{\prime}+w x y z^{\prime}+w^{\prime} x y^{\prime} z$$

Find the DNF of each boolean function. $$f(x, y, z)=x \uparrow(y \uparrow z)$$

Construct a logic table for each boolean function defined by each boolean expression. $$x y z+x(y z)^{\prime}$$

The set \(D_{70}=\\{1,2,5,7,10,14,35,70\\}\) of positive factors of 70 is a boolean algebra under the operations \(\oplus, \odot,\) and ' defined by \(x \oplus y=\operatorname{lcm}\\{x, y\\}\) \(x \odot y=\operatorname{gcd}\\{x, y\\},\) and \(x^{\prime}=70 / x .\) Compute each. $$(5 \oplus 7)^{\prime}$$

The set \(D_{70}=\\{1,2,5,7,10,14,35,70\\}\) of positive factors of 70 is a boolean algebra under the operations \(\oplus, \odot,\) and ' defined by \(x \oplus y=\operatorname{lcm}\\{x, y\\}\) \(x \odot y=\operatorname{gcd}\\{x, y\\},\) and \(x^{\prime}=70 / x .\) Compute each. $$5^{\prime} \odot 7^{\prime}$$

Construct a logic table for each boolean function defined by each boolean expression. $$x^{\prime} y z^{\prime}+x^{\prime}(y z)^{\prime}$$

Find the DNF of each boolean function. $$f(x, y, z)=(x \uparrow y) \uparrow z$$

Simplify each boolean expression using the laws of boolean algebra. $$w x^{\prime} y z+w x^{\prime} y z^{\prime}+w^{\prime} x^{\prime} y z^{\prime}+w^{\prime} x y z^{\prime}$$

Find the DNF of each boolean function. $$f(x, y, z)=(x \uparrow y) \uparrow z$$

The set \(D_{70}=\\{1,2,5,7,10,14,35,70\\}\) of positive factors of 70 is a boolean algebra under the operations \(\oplus, \odot,\) and ' defined by \(x \oplus y=\operatorname{lcm}\\{x, y\\}\) \(x \odot y=\operatorname{gcd}\\{x, y\\},\) and \(x^{\prime}=70 / x .\) Compute each. $$\left(7 \odot 2^{\gamma}\right.$$