GATE CSE 2022 | GA Question: 4

Question

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.

• A. Statement $1$ and Statement $3$
• B. Statement $1$ and Statement $2$
• C. Statement $2$ and Statement $4$
• D. Statement $3$ and Statement $4$

Answer 1

Statement 1 implies

Statement 3 implies

Both cannot be true simultaneously.

So option A is the answer.

For all other options we can make the given statements true simultaneously.

Answer 2

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 $:\text{A}$

Answer 3

Answer: 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.

Answer 4

Option A :

The two statements that cannot be true simultaneously are "All students are inquisitive" and "No student is inquisitive".