Construct a truth table for [p A (p→q)] → q.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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ANSWER #5
![**Analyze and answer the following statements.**
1. **State whether each bi-conditional is true or false.**
a. \( x > 7 \) if and only if \( x > 6 \)
b. \( x + 5 > 7 \) if and only if \( x > 2 \)
2. **Use \( p, q, \) and \( r \) as defined in Example 6. Write the following symbolic statements in words:**
a. \( p \leftrightarrow \sim r \)
b. \( \sim q \leftrightarrow \sim r \)
3. **Write the negation of each conditional statement.**
a. If I finish the report, I will go to the concert.
b. If the square of \( n \) is 25, then \( n \) is 5 or -5.
4. **Write each of the following in its equivalent disjunctive form.**
a. If I don’t move to Georgia, I will live in Houston.
b. If the number is divisible by 2, then the number is even.
5. **Construct a truth table for \([p \land (p \rightarrow q)] \rightarrow q\).**
6. **Determine the truth value of each of the following conditional statements.**
a. If \( 4 \geq 3 \), then \( 2 + 5 = 6 \)
b. If \( 5 > 9 \), the \( 4 > 9 \)
c. If Tuesday follows Monday, then April follows March.
7. **Identify the antecedent and consequent in each of the following conditional statements.**
a. If I study for at least 6 hours, then I will get an A on the test.
b. If I get the job, I will buy a new car.
c. If you can dream it, you can do it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0928574a-9889-491a-94d3-3c8961bcc52e%2F828891ec-3ea7-4978-8948-9a374f9cbd11%2F3jqb7d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Analyze and answer the following statements.**
1. **State whether each bi-conditional is true or false.**
a. \( x > 7 \) if and only if \( x > 6 \)
b. \( x + 5 > 7 \) if and only if \( x > 2 \)
2. **Use \( p, q, \) and \( r \) as defined in Example 6. Write the following symbolic statements in words:**
a. \( p \leftrightarrow \sim r \)
b. \( \sim q \leftrightarrow \sim r \)
3. **Write the negation of each conditional statement.**
a. If I finish the report, I will go to the concert.
b. If the square of \( n \) is 25, then \( n \) is 5 or -5.
4. **Write each of the following in its equivalent disjunctive form.**
a. If I don’t move to Georgia, I will live in Houston.
b. If the number is divisible by 2, then the number is even.
5. **Construct a truth table for \([p \land (p \rightarrow q)] \rightarrow q\).**
6. **Determine the truth value of each of the following conditional statements.**
a. If \( 4 \geq 3 \), then \( 2 + 5 = 6 \)
b. If \( 5 > 9 \), the \( 4 > 9 \)
c. If Tuesday follows Monday, then April follows March.
7. **Identify the antecedent and consequent in each of the following conditional statements.**
a. If I study for at least 6 hours, then I will get an A on the test.
b. If I get the job, I will buy a new car.
c. If you can dream it, you can do it.
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