A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: ‘Exactly n of the statements on this sheet are false.’ Which statements are true and which are false?	Choose the correct option.
A) The even numbered statements are true and the odd numbered statements are false.	B) The odd numbered statements are true and the even numbered statements are false.	C) All the statements are false.	D) The 39th statement is true and the rest are false	E) The 69th statement is true and the rest are false
Assume there is only one statement is there. The statement should read "Exactly 1 statement on this sheet is false" . If the truth value of the statement is true, then given statement should be false. This is contradiction. If the statement is false, Then the given statement is true. but there is not other true statement.   Assume there are two statements. By the above logic, 2nd statement should not be true. But 1st statement is true as it truthfully says the truthfulness. The odd numbered statements are true and the even numbered statements are false.y this logic we know that If there are "n" statements, (n-1)th statement is the only true statement And all other are false   Answer:The odd numbered statements are true and the even numbered statements are false.
<result>B</result>
A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: ‘Exactly n of the statements on this sheet are false.’ Which statements are true and which are false?