To determine the number of rows in the truth table for the compound statement:
[tex]$
[(q \wedge \sim v) \wedge(r \vee t \wedge \sim p)] \wedge(\sim u \wedge \sim s)
$[/tex]
we need to follow these steps:
1. Identify the unique propositions in the statement: The given compound statement contains the propositions [tex]\( q, v, r, t, p, u, \)[/tex] and [tex]\( s \)[/tex].
2. Count the unique propositions: In this statement, there are 6 unique propositions.
3. Calculate the number of rows in the truth table: The number of rows in a truth table is determined by the number of unique propositions. For [tex]\( n \)[/tex] unique propositions, the truth table will have [tex]\( 2^n \)[/tex] rows.
Given that there are 6 unique propositions:
[tex]\[
2^6 = 64
\][/tex]
Therefore, the truth table consists of [tex]\(\boxed{64}\)[/tex] rows.
