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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 $\text{CANNOT BE TRUE}$ simultaneously, assuming that there is at least one student in the class.

1. Statement $1$ and Statement $3$
2. Statement $1$ and Statement $2$
3. Statement $2$ and Statement $4$
4. Statement $3$ and Statement $4$

Statement 1 seems like this.

Statement 3 look like this .

both cannot be true simultaneously.

So option A is the answer.

For other option they are possible.

Given below are four statements. We can draw the Venn diagram for each of them.

• 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.

We can clearly see ${\color{Blue}{\text{statement 1, and statement 3}}}$ can not be possible at the same time.

Correct Answer $:\text{A}$

There will be no class with all students who does not have interest in learning and also no class with all the students who have interest in learning.