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How do you use truth tables to determine whether or not the following pairs of statements are logically equivalent?

i) (p ᴧ q)→r ii) p→(q→r)

I'm confused on how you would do that, Thanks

frabala
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Roy Kesserwani
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    You compute the truth table of each statement and compare values. If the two truth tables agree at each row, then the statements are equivalent. If not, then they are not. – Ittay Weiss Feb 17 '14 at 09:24

1 Answers1

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$p$, $q$ and $r$ are variables that can take either value $T$ (true) or value $F$ (false). You have to consider what happens for each combination of values for $p$, $q$ and $r$. A table showing the cases is very helpful.

For example, for the first statement, a part of the table is: \begin{array}{|c|c}\\ \hline p & r & q & p\wedge q & (p\wedge q)\to r\\ \hline T & T & T & T & T\\ T & T & F & T & F\\ T & F & T & F & T\\ \vdots&\vdots&\vdots&\vdots&\vdots \end{array}

Then you do a similar table for the second statement. If for for all combinations of values on $p$, $q$ and are, the two statements end up with the same value, then the two statements are logically equivalent.

frabala
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