Give the number of rows in the truth table for the following compound statement.
\[
[(\sim p \wedge \sim u) \wedge(\sim r \wedge q \vee \sim s)] \vee(\sim t \vee \sim v)
\]
The truth table consists of rows. (Type à whole number.)
Answer
Final Answer: The number of rows in the truth table for the given compound statement is \(\boxed{128}\).
Step 1 ：Identify the unique variables in the compound statement. In this case, the unique variables are p, u, r, q, s, t, v.
Step 2 ：Each variable can take on two values, true or false. Therefore, the number of rows in the truth table is \(2^n\), where n is the number of unique variables.
Step 3 ：In this case, n is 7. So, the number of rows in the truth table is \(2^7\).
Step 4 ：Calculate \(2^7\) to get the final answer.
Step 5 ：Final Answer: The number of rows in the truth table for the given compound statement is \(\boxed{128}\).
