# Math Help - logic

1. ## logic

Dear All,

please help me solving this question i have urgent assigment to submit any help well be appriated.

Question. Convert the following theorem to logical and prove them by constructing truth table:
(A Ç B)¢ = A¢È B¢

2. Hello, zeeshan4u3!

Convert the following theorem to logical and prove by truth table:

. . . $(A \cap B)' \:=\:A' \cup B'$
In logic, we have: . $\sim(p \wedge q) \:\leftrightarrow \:\sim p \:\vee \sim q$

. . $\begin{array}{c|c||cccccccc}
p & q & \sim & (p & \wedge & q) & \leftrightarrow & \sim p & \vee & \sim q \\ \hline
T & T & F & T & T & T & {\color{blue}T} & F & F & F \\
T & F & T & T & F & F & {\color{blue}T} & F & T & T \\
F & T & T & F & F & T & {\color{blue}T} & T & T & F \\
F & F & T & F & F & F & {\color{blue}T} & T & T & T \\ \hline
& & 3 & 1 & 2 & 1 & 4 & 1 & 3 & 1
\end{array}$

3. Thanks alot Prof.Soroban

can i suppose its my question answer or its just an example.