Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.