Worksheet featuring six math problems requiring students to write counterexamples for given statements.
Worksheet with six counterexample problems for practice, titled "Practice Problems" and generated by www.easyworksheet.com.
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Step-by-step solution for: Write the Counterexample Problems Worksheet for 7th - Higher Ed ...
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Show Answer Key & Explanations
Step-by-step solution for: Write the Counterexample Problems Worksheet for 7th - Higher Ed ...
The worksheet provided involves writing counterexamples for given statements. A counterexample is an example that disproves a statement or shows that it is not always true. Let's solve each problem step by step.
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Statement: If the project is due on Friday, then it is not 1:00 PM.
Counterexample:
To disprove this statement, we need to find a situation where the project is due on Friday and it is 1:00 PM.
- Example: The project is due on Friday at 1:00 PM.
This directly contradicts the statement because it shows that the project can be due on Friday while it is 1:00 PM.
Answer: The project is due on Friday at 1:00 PM.
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Statement: If I wear shoes and then Ralph likes candy.
Counterexample:
To disprove this statement, we need to show a situation where you wear shoes but Ralph does not like candy.
- Example: You wear shoes, but Ralph dislikes candy.
This shows that wearing shoes does not necessarily mean Ralph likes candy.
Answer: You wear shoes, but Ralph dislikes candy.
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Statement: If I am using the web then the Wi-Fi does not work.
Counterexample:
To disprove this statement, we need to show a situation where you are using the web and the Wi-Fi is working.
- Example: You are using the web, and the Wi-Fi is functioning properly.
This contradicts the statement because it shows that using the web does not imply the Wi-Fi is not working.
Answer: You are using the web, and the Wi-Fi is working.
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Statement: If I leave school then it is 1:00 PM.
Counterexample:
To disprove this statement, we need to show a situation where you leave school but it is not 1:00 PM.
- Example: You leave school at 3:00 PM.
This contradicts the statement because leaving school does not necessarily mean it is 1:00 PM.
Answer: You leave school at 3:00 PM.
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Statement: If Peter forces like candy then Mel does not like surfing.
Counterexample:
To disprove this statement, we need to show a situation where Peter forces like candy and Mel still likes surfing.
- Example: Peter forces like candy, and Mel enjoys surfing.
This contradicts the statement because it shows that Peter liking candy does not imply Mel does not like surfing.
Answer: Peter forces like candy, and Mel likes surfing.
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Statement: If yesterday was Friday then Ann doesn't go to the party.
Counterexample:
To disprove this statement, we need to show a situation where yesterday was Friday but Ann still goes to the party.
- Example: Yesterday was Friday, and Ann attends the party.
This contradicts the statement because it shows that yesterday being Friday does not necessarily mean Ann doesn't go to the party.
Answer: Yesterday was Friday, and Ann goes to the party.
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1. The project is due on Friday at 1:00 PM.
2. You wear shoes, but Ralph dislikes candy.
3. You are using the web, and the Wi-Fi is working.
4. You leave school at 3:00 PM.
5. Peter forces like candy, and Mel likes surfing.
6. Yesterday was Friday, and Ann goes to the party.
Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & \text{The project is due on Friday at 1:00 PM.} \\
2. & \text{You wear shoes, but Ralph dislikes candy.} \\
3. & \text{You are using the web, and the Wi-Fi is working.} \\
4. & \text{You leave school at 3:00 PM.} \\
5. & \text{Peter forces like candy, and Mel likes surfing.} \\
6. & \text{Yesterday was Friday, and Ann goes to the party.} \\
\end{array}
}
\]
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Problem 1:
Statement: If the project is due on Friday, then it is not 1:00 PM.
Counterexample:
To disprove this statement, we need to find a situation where the project is due on Friday and it is 1:00 PM.
- Example: The project is due on Friday at 1:00 PM.
This directly contradicts the statement because it shows that the project can be due on Friday while it is 1:00 PM.
Answer: The project is due on Friday at 1:00 PM.
---
Problem 2:
Statement: If I wear shoes and then Ralph likes candy.
Counterexample:
To disprove this statement, we need to show a situation where you wear shoes but Ralph does not like candy.
- Example: You wear shoes, but Ralph dislikes candy.
This shows that wearing shoes does not necessarily mean Ralph likes candy.
Answer: You wear shoes, but Ralph dislikes candy.
---
Problem 3:
Statement: If I am using the web then the Wi-Fi does not work.
Counterexample:
To disprove this statement, we need to show a situation where you are using the web and the Wi-Fi is working.
- Example: You are using the web, and the Wi-Fi is functioning properly.
This contradicts the statement because it shows that using the web does not imply the Wi-Fi is not working.
Answer: You are using the web, and the Wi-Fi is working.
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Problem 4:
Statement: If I leave school then it is 1:00 PM.
Counterexample:
To disprove this statement, we need to show a situation where you leave school but it is not 1:00 PM.
- Example: You leave school at 3:00 PM.
This contradicts the statement because leaving school does not necessarily mean it is 1:00 PM.
Answer: You leave school at 3:00 PM.
---
Problem 5:
Statement: If Peter forces like candy then Mel does not like surfing.
Counterexample:
To disprove this statement, we need to show a situation where Peter forces like candy and Mel still likes surfing.
- Example: Peter forces like candy, and Mel enjoys surfing.
This contradicts the statement because it shows that Peter liking candy does not imply Mel does not like surfing.
Answer: Peter forces like candy, and Mel likes surfing.
---
Problem 6:
Statement: If yesterday was Friday then Ann doesn't go to the party.
Counterexample:
To disprove this statement, we need to show a situation where yesterday was Friday but Ann still goes to the party.
- Example: Yesterday was Friday, and Ann attends the party.
This contradicts the statement because it shows that yesterday being Friday does not necessarily mean Ann doesn't go to the party.
Answer: Yesterday was Friday, and Ann goes to the party.
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Final Answers:
1. The project is due on Friday at 1:00 PM.
2. You wear shoes, but Ralph dislikes candy.
3. You are using the web, and the Wi-Fi is working.
4. You leave school at 3:00 PM.
5. Peter forces like candy, and Mel likes surfing.
6. Yesterday was Friday, and Ann goes to the party.
Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & \text{The project is due on Friday at 1:00 PM.} \\
2. & \text{You wear shoes, but Ralph dislikes candy.} \\
3. & \text{You are using the web, and the Wi-Fi is working.} \\
4. & \text{You leave school at 3:00 PM.} \\
5. & \text{Peter forces like candy, and Mel likes surfing.} \\
6. & \text{Yesterday was Friday, and Ann goes to the party.} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of counterexample worksheet.
