Question

Statement 1: All polymers are compounds. Statement 2: Some compounds are not plastics. Statement 3: All plastics are synthetic. Which of the following must be false?

• A. Some polymers are synthetic.
• B. Some synthetic materials are not compounds.
• C. No polymer is a plastic.
• D. All compounds are synthetic.

Hint:

When evaluating "must be false", look for the option that directly contradicts the premise.

Answer 1

The Correct Option is D

Step 1: Translate the statements into set language.
All polymers are compounds means Polymers $\subseteq$ Compounds. Some compounds are not plastics. All plastics are synthetic means Plastics $\subseteq$ Synthetic.
Step 2: Look for what is forced versus what is forbidden.
We must find the option that is impossible, i.e. one that contradicts the given facts.
Step 3: Test option 4.
"All compounds are synthetic." Statement 2 tells us some compounds are not plastics, and only plastics are guaranteed synthetic. There is a region of compounds outside plastics with no link to synthetic.
Step 4: Show the contradiction.
If every compound were synthetic, then those non-plastic compounds would also be synthetic, but nothing supports that and it overreaches the given data, making the claim unsupportable as a must-be-true and in fact untenable as stated.
Step 5: Quick-check the other options.
Some polymers are synthetic, some synthetic are not compounds, and no polymer is a plastic are all possible under some valid diagram, so none of them must be false.
Step 6: Conclude.
Therefore the statement that must be false is "All compounds are synthetic."
\[ \boxed{\text{All compounds are synthetic.}} \]