Originally Posted by

**Soroban** Hello, ironz!

It sounds like this is your first truth table . . . is it?

You are off to a good start.

Your initial set-up is correct:

. . $\displaystyle \begin{array}{|c|c||c|c||x|x}

p & q & \sim p & \sim q & \sim p\:\vee\sim q \\ \hline

T & T & F & F & \\ T & F & F & T & \\ F & T & T & F & \\ F & F & T & T & \\ \hline

_1 & _2 & _3 & _4 & _5 \\ \hline \end{array}$

Now you want an "or" between columns 3 and 4.

You're expected to when an "or" (disjunction) is true.

. . . . . $\displaystyle \begin{array}{cccc}T \vee T &=& T \\ T \vee F &=& T \\ F \vee T &=& T \\ F \vee F &=& F \end{array}$

Now you can complete the fifth column:

. . $\displaystyle \begin{array}{|c|c||c|c||x|x}

p & q & \sim p & \sim q & \sim p\:\vee\sim q \\ \hline

T & T & F & F & {\bf F} \\ T & F & F & T & {\bf T} \\ F & T & T & F & {\bf T} \\ F & F & T & T & {\bf T} \\ \hline

_1 & _2 & _3 & _4 & _5 \\ \hline \end{array}$