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Magazine Problem 31
Is \(\langle S, \cup, \cap,, \emptyset, U)\) a boolean algebra for each subset \(S\) of \(P(U),\) where \(U=[a, b, c] ?\) $$ \\{\emptyset,[a|,| b, c |, U\\} $$
Problem 31
Find the DNFs of the boolean functions $$\begin{array}{|ccc||c|} \hline \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} & \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}) \\ \hline 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ \hline \end{array}$$
Problem 31
Is \(\left\langle S, \cup, \cap,^{\prime}, \emptyset, U\right\rangle\) a boolean algebra for each subset \(S\) of \(P(U),\) where \(U=\\{a, b, c\\} ?\) $$\\{\emptyset,|a|,\\{b, c\\}, U\\}$$
Problem 31
Using a Karnaugh map, simplify each boolean expression. $$x y^{\prime} z^{\prime}+x y^{\prime} z+x^{\prime} y^{\prime} z^{\prime}+x^{\prime} y^{\prime} z$$
Problem 32
Using a Karnaugh map, simplify each boolean expression. $$x y z+x y z^{\prime}+x^{\prime} y^{\prime} z^{\prime}+x^{\prime} y^{\prime} z$$
Problem 32
Find the DNFs of the boolean functions $$\begin{array}{|ccc||c|} \hline x & y & z & f(x, y, z) \\ \hline 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0 \\ \hline \end{array}$$
Problem 32
Is \(\left\langle S, \cup, \cap,^{\prime}, \emptyset, U\right\rangle\) a boolean algebra for each subset \(S\) of \(P(U),\) where \(U=\\{a, b, c\\} ?\) $$\\{\emptyset, | a\\},\\{b\\},\\{a, b\\}, U\\}$$
Problem 32
Is \(\langle S, \cup, \cap,, \emptyset, U)\) a boolean algebra for each subset \(S\) of \(P(U),\) where \(U=[a, b, c] ?\) $$ \\{\emptyset,|a|,|b|,\\{a, b |, U\\} $$
Problem 33
Find the DNFs of the boolean functions $$\begin{array}{|ccc||c|} \hline x & y & z & f(x, y, z) \\ \hline 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 \\ \hline \end{array}$$
Problem 33
Is \(\langle S, \cup, \cap,, \emptyset, U)\) a boolean algebra for each subset \(S\) of \(P(U),\) where \(U=[a, b, c] ?\) $$ \\{O,\\{b\\},[a, c], U\\} $$
