A convenient and helpful way to organize truth values of various statements is in a truth table. A truth table is a table whose columns are statements, and whose rows are possible scenarios. The table contains every possible scenario and the truth values that would occur. One of the simplest truth tables records the truth values for a statement and its negation.

Figure %: The truth table for
*p*
,
âàü*p*

Truth tables get a little more complicated when conjunctions and
disjunctions of statements are included. Below is the truth table for
*p*
,
*q*
,
*p*âàç*q*
,
*p*âàè*q*
.
Notice that all the values are correct, and all possibilities are accounted for.

Figure %: The truth table for
*p*
,
*q*
,
*p*âàç*q*
,
*p*âàè*q*

The truth table for an implication, or conditional statement looks like this:

Figure %: The truth table for
*p*
,
*q*
,
*p*âá’*q*

Now that the truth table for a standard conditional statement is understood, we'll take a look at the truth table for its inverse, converse, and contrapositive.

Figure %: The truth table for an implication and its inverse, converse, and
contrapositive

One more thing should be said of truth tables: they can hold more than two
different statements. You could have
*p*
,
*q*
,
*r*
,
*s*
, and
*t*
in the same truth table.
There would then be 32 possible scenarios (
2^{5}
), so the table would have 5
columns and 32 rows.

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