# logic

• Nov 3rd 2008, 09:30 PM
zeeshan4u3
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¢
• Nov 3rd 2008, 10:27 PM
Soroban
Hello, zeeshan4u3!

Quote:

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

. . . $\displaystyle (A \cap B)' \:=\:A' \cup B'$

In logic, we have: .$\displaystyle \sim(p \wedge q) \:\leftrightarrow \:\sim p \:\vee \sim q$

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

• Nov 3rd 2008, 10:30 PM
zeeshan4u3
Thanks alot Prof.Soroban

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