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Give the number of rows in the truth table for the following compound statement.

[tex]\[
[(q \wedge \sim v) \wedge (r \vee t \wedge \sim p)] \wedge (\sim u \wedge \sim s)
\][/tex]

The truth table consists of [tex]$\square$[/tex] rows. (Type a whole number.)

Sagot :

GinnyAnswer
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.
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