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Magazine Problem 17
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. $$\left(7 \odot 2^{\gamma}\right.$$
Problem 18
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. $$7^{\prime} \oplus 2^{\prime}$$
Problem 19
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. $$10 \oplus 10$$
Problem 19
Using a logic table, verify each. $$(x+y)^{\prime}=x^{\prime} y^{\prime}$$
Problem 19
Mark each statement as true or false. $$x \uparrow y=y \uparrow x$$
Problem 20
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. $$7 \odot 7$$
Problem 20
Find the boolean expression represented by each Karnaugh map.
Problem 20
Mark each statement as true or false. $$x \downarrow y=y \downarrow x$$
Problem 20
Using a logic table, verify each. $$(x y)^{\prime}=x^{\prime}+y^{\prime}$$
Problem 20
Mark each statement as true or false. $$x\downarrow y=y \downarrow x$$
