Which of the following statements follows the conclusion?Conclusions:Some A's are CSome C's are EStatements:Statements – 1: Some A’s are B’s. Some B’s are C’s. No C is D. No D is E.Statements – 2: All A’s are B’s. All B’s are C’s. Some C’s are D’s. All D’s are E’sStatements – 3: Some A’s are B’s. All B’s are C’s. Some C’s are D’s. All D’s are E’sStatements – 4: All A’s are B’s. Some B’s are C’s. No C is D. All D’s are E’sStatements – 5: All A’s are B’s. All B’s are C’s. No C is D. All D’s are E’s
Question
Which of the following statements follows the conclusion?Conclusions:Some A's are CSome C's are EStatements:Statements – 1: Some A’s are B’s. Some B’s are C’s. No C is D. No D is E.Statements – 2: All A’s are B’s. All B’s are C’s. Some C’s are D’s. All D’s are E’sStatements – 3: Some A’s are B’s. All B’s are C’s. Some C’s are D’s. All D’s are E’sStatements – 4: All A’s are B’s. Some B’s are C’s. No C is D. All D’s are E’sStatements – 5: All A’s are B’s. All B’s are C’s. No C is D. All D’s are E’s
Solution
The statement that follows the conclusion "Some A's are C" and "Some C's are E" is Statement – 3: Some A’s are B’s. All B’s are C’s. Some C’s are D’s. All D’s are E’s.
Here's the step by step reasoning:
- Some A's are B's: This means there is at least one A that is also B.
- All B's are C's: This means every B is also a C. So, the A's that are B's are also C's. Hence, some A's are C's.
- Some C's are D's: This means there is at least one C that is also D.
- All D's are E's: This means every D is also an E. So, the C's that are D's are also E's. Hence, some C's are E's.
Therefore, Statement 3 follows the conclusion.
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