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If some A are B and all B are C, which of the following must be true?

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Question: If some A are B and all B are C, which of the following must be true?

Options:

  1. All A are C
  2. Some A are not C
  3. Some C are A
  4. No A are C

Correct Answer: All A are C

Solution: 

If some A are B and all B are C, then it follows that some A must also be C.

If some A are B and all B are C, which of the following must be true?

Practice Questions

Q1
If some A are B and all B are C, which of the following must be true?
  1. All A are C
  2. Some A are not C
  3. Some C are A
  4. No A are C

Questions & Step-by-Step Solutions

If some A are B and all B are C, which of the following must be true?
  • Step 1: Understand the terms. 'Some A are B' means there is at least one A that is also a B.
  • Step 2: Understand the second part. 'All B are C' means every B is also a C.
  • Step 3: Combine the information. Since some A are B, and all B are C, the A that are B must also be C.
  • Step 4: Conclusion. Therefore, it must be true that some A are also C.
  • Logical Deduction – The ability to infer conclusions from given premises using logical reasoning.
  • Quantifiers in Logic – Understanding the implications of 'some' and 'all' in logical statements.
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