Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

Question

Twenty girls are sitting in a row. A girl is shifted by four places towards the left, then she became 8th from the left end. The earlier position of that girl from the right end of the row is

Answer 1

To solve the problem of identifying which two statements cannot be true simultaneously, we need to analyze each statement logically.

Statement 1: "All students are inquisitive." - This statement means every student in the class is inquisitive. There are no exceptions.
Statement 2: "Some students are inquisitive." - This statement implies there is at least one student who is inquisitive, but not necessarily all students are inquisitive.
Statement 3: "No student is inquisitive." - This statement suggests that not a single student in the class is inquisitive.
Statement 4: "Some students are not inquisitive." - This indicates that there exists at least one student who is not inquisitive.

Now, let's evaluate the combinations:

Statement 1 and Statement 3: If all students are inquisitive (Statement 1), it is impossible for no student to be inquisitive (Statement 3). Thus, these two statements cannot be true at the same time.
Statement 1 and Statement 2: Statement 2 is a weaker statement compared to Statement 1. If all students are inquisitive, then certainly some students are inquisitive, making these two statements compatible.
Statement 2 and Statement 4: If some students are inquisitive (Statement 2), it is possible that some students are not inquisitive, making these two statements possible simultaneously.
Statement 3 and Statement 4: If no student is inquisitive (Statement 3), it definitely includes some students are not inquisitive, thus these two statements are compatible.

Thus, the correct answer is: Statement 1 and Statement 3 cannot be true simultaneously.

Answer 2

To solve the problem of identifying which two statements cannot be true simultaneously, we need to analyze each statement logically.

Statement 1: "All students are inquisitive." - This statement means every student in the class is inquisitive. There are no exceptions.
Statement 2: "Some students are inquisitive." - This statement implies there is at least one student who is inquisitive, but not necessarily all students are inquisitive.
Statement 3: "No student is inquisitive." - This statement suggests that not a single student in the class is inquisitive.
Statement 4: "Some students are not inquisitive." - This indicates that there exists at least one student who is not inquisitive.

Now, let's evaluate the combinations:

Statement 1 and Statement 3: If all students are inquisitive (Statement 1), it is impossible for no student to be inquisitive (Statement 3). Thus, these two statements cannot be true at the same time.
Statement 1 and Statement 2: Statement 2 is a weaker statement compared to Statement 1. If all students are inquisitive, then certainly some students are inquisitive, making these two statements compatible.
Statement 2 and Statement 4: If some students are inquisitive (Statement 2), it is possible that some students are not inquisitive, making these two statements possible simultaneously.
Statement 3 and Statement 4: If no student is inquisitive (Statement 3), it definitely includes some students are not inquisitive, thus these two statements are compatible.

Thus, the correct answer is: Statement 1 and Statement 3 cannot be true simultaneously.

Show Hint

The Correct Option is A

Solution and Explanation

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