## Related questions with answers

Find a logic statement involving p and q that generates each of the following truth tables .

$\left[\begin{array}{lll} p & q & ?\\ \hline T & T & T\\ T & F & F\\ F & T & T\\ F & F & T \end{array}\right]$

Solution

VerifiedGuided by the fact that only the conjunction $T\wedge T$ is true, we seek out rows where the last entry is true.

We find three such rows, and only one yields F (false), so we change the focus of our search.

We find that combination (that yields false) and invert it.

"$?$" is false for ( p is true) and (q is false) so,

( p) and not(q) will yield a false value.

Inverting, by DeMorgan's Law, the statement ( p) and not(q), we have

"$?$" $=\sim(p\wedge\sim q)=\quad$... apply DeMorgan's Law

"$?$" $=(\sim p)\vee[\sim(\sim q)]=\sim p\vee q.

$

Check the truth values, row by row, and note the results: T,F,T,T, as they should be.

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