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please help me solving this question i have urgent assigment to submit any help well be appriated.
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Question. Convert the following theorem to logical and prove them by constructing truth table:
(A Ç B)¢ = A¢È B¢
Hello, zeeshan4u3!
In logic, we have: .$\displaystyle \sim(p \wedge q) \:\leftrightarrow \:\sim p \:\vee \sim q$Convert the following theorem to logical and prove by truth table:
. . . $\displaystyle (A \cap B)' \:=\:A' \cup B' $
. . $\displaystyle \begin{array}{c|c||cccccccc}
p & q & \sim & (p & \wedge & q) & \leftrightarrow & \sim p & \vee & \sim q \\ \hline
T & T & F & T & T & T & {\color{blue}T} & F & F & F \\
T & F & T & T & F & F & {\color{blue}T} & F & T & T \\
F & T & T & F & F & T & {\color{blue}T} & T & T & F \\
F & F & T & F & F & F & {\color{blue}T} & T & T & T \\ \hline
& & 3 & 1 & 2 & 1 & 4 & 1 & 3 & 1
\end{array}$