Question

Question [This is the stem.] (8 points)
p q r
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

what is the p AND (NOT q OR r)

Answer 1

To evaluate the expression \( p \) AND \( (NOT q OR r) \) for each combination of the variables \( p \), \( q \), and \( r \) shown in the truth table, we will calculate the result step by step for each row.

First, let's define the operations:
- \( NOT q \): The negation of the value of \( q \).
- \( OR \): The logical disjunction which is true if at least one operand is true.
- \( AND \): The logical conjunction which is true only if both operands are true.

Now, let's calculate \( p \) AND \( (NOT q OR r) \) for each case:

1. **Row: \( p = 0 \), \( q = 0 \), \( r = 0 \)**
- \( NOT q = 1 \)
- \( (NOT q OR r) = 1 OR 0 = 1 \)
- Result: \( 0 AND 1 = 0 \)

2. **Row: \( p = 0 \), \( q = 0 \), \( r = 1 \)**
- \( NOT q = 1 \)
- \( (NOT q OR r) = 1 OR 1 = 1 \)
- Result: \( 0 AND 1 = 0 \)

3. **Row: \( p = 0 \), \( q = 1 \), \( r = 0 \)**
- \( NOT q = 0 \)
- \( (NOT q OR r) = 0 OR 0 = 0 \)
- Result: \( 0 AND 0 = 0 \)

4. **Row: \( p = 0 \), \( q = 1 \), \( r = 1 \)**
- \( NOT q = 0 \)
- \( (NOT q OR r) = 0 OR 1 = 1 \)
- Result: \( 0 AND 1 = 0 \)

5. **Row: \( p = 1 \), \( q = 0 \), \( r = 0 \)**
- \( NOT q = 1 \)
- \( (NOT q OR r) = 1 OR 0 = 1 \)
- Result: \( 1 AND 1 = 1 \)

6. **Row: \( p = 1 \), \( q = 0 \), \( r = 1 \)**
- \( NOT q = 1 \)
- \( (NOT q OR r) = 1 OR 1 = 1 \)
- Result: \( 1 AND 1 = 1 \)

7. **Row: \( p = 1 \), \( q = 1 \), \( r = 0 \)**
- \( NOT q = 0 \)
- \( (NOT q OR r) = 0 OR 0 = 0 \)
- Result: \( 1 AND 0 = 0 \)

8. **Row: \( p = 1 \), \( q = 1 \), \( r = 1 \)**
- \( NOT q = 0 \)
- \( (NOT q OR r) = 0 OR 1 = 1 \)
- Result: \( 1 AND 1 = 1 \)

Now, let's summarize the results for each row:

\[
\begin{array}{|c|c|c|c|}
\hline
p & q & r & p \text{ AND } (NOT q \text{ OR } r) \\
\hline
0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 \\
0 & 1 & 1 & 0 \\
1 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 \\
1 & 1 & 0 & 0 \\
1 & 1 & 1 & 1 \\
\hline
\end{array}
\]

Thus, the final results for \( p \) AND \( (NOT q OR r) \) are:
- 0, 0, 0, 0, 1, 1, 0, 1 for the respective rows.