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Can someone help me with this truth table. I just don't understand how to do it.

Can someone help me with this truth table. I just don't understand how to do it.-example-1
User Arik Kfir
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An implication
(p\implies q) is true if either the premise
(p) is false, or both the premise and conclusion
(p\text{ and }q) are both true, and false otherwise.


\begin{array}cp&q&p\implies q&\\eg q&(p\implies q)\land\\eg q&\\eg p&(p\implies q)\land\\eg q\implies\\eg p\\T&T&T&&&&\\T&F&F&&&&\\F&T&T&&&&\\F&F&T&&&&\end{array}

Negation
(\\eg q) is straightforward; if a statement is true, then its negation is false, and vice versa.


\begin{array}cp&q&p\implies q&\\eg q&(p\implies q)\land\\eg q&\\eg p&(p\implies q)\land\\eg q\implies\\eg p\\T&T&T&F&&F\\T&F&F&T&&F\\F&T&T&F&&T\\F&F&T&T&&T\end{array}

A conjunction
(p\land q) is true if both premises are true, and false otherwise.


\begin{array}cp&q&p\implies q&\\eg q&(p\implies q)\land\\eg q&\\eg p&(p\implies q)\land\\eg q\implies\\eg p\\T&T&T&F&F&F\\T&F&F&T&F&F\\F&T&T&F&F&T\\F&F&T&T&T&T\end{array}

Finally, by the rules of implication, we can fill the last column:


\begin{array}cp&q&p\implies q&\\eg q&(p\implies q)\land\\eg q&\\eg p&(p\implies q)\land\\eg q\implies\\eg p\\T&T&T&F&F&F&T\\T&F&F&T&F&F&T\\F&T&T&F&F&T&T\\F&F&T&T&T&T&T\end{array}

User NETQuestion
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