If the statement 'All cricketers are rich persons' is given as true which of the following statements can be inferred to be false?

A. No cricketers are rich persons.

B. Some cricketers are rich persons.

C. Some cricketers are not rich persons.

D. Some rich persons are cricketers.

Choose the correct answer from the options given below:

Key Points

• If the statement "All cricketers are rich persons" is given as true, it means that every cricketer is a rich person. Based on this information, the following statements can be inferred:

A. No cricketers are rich persons.

• This statement is false because it contradicts the given information.
• If all cricketers are rich persons, then it implies that there are cricketers who are rich.

B. Some cricketers are rich persons.

• This statement is true because it is consistent with the given information.
• If all cricketers are rich persons, then it implies that there are cricketers who are indeed rich.

C. Some cricketers are not rich persons.

• This statement is false because it contradicts the given information.
• If all cricketers are rich persons, then it implies that there are no cricketers who are not rich.

D. Some rich persons are cricketers.

• This statement cannot be inferred from the given information. While it is possible that some rich persons are cricketers, it is not necessarily implied by the statement "All cricketers are rich persons."

Therefore, the correct answer is option 2) A and C Only.