# GATE Mechanical 2022 Set 1 | GA Question: 9

1 vote

​​​​​​Given below are three conclusions drawn based on the following three statements.

Statement $1$ : All teachers are professors.
Statement $2$ : No professor is a male.
Statement $3$ : Some males are engineers.

Conclusion $\text{I}$: No engineer is a professor.
Conclusion $\text{II}$: Some engineers are professors.
Conclusion $\text{III}$: No male is a teacher.

Which one of the following options can be logically inferred?

1. Only conclusion $\text{III}$ is correct
2. Only conclusion $\text{I}$ and conclusion $\text{II}$ are correct
3. Only conclusion $\text{II}$ and conclusion $\text{III}$ are correct
4. Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct

edited

Given that,

• Statement $1$: All teachers are professors.
• Statement $2$: No professor is a male.
• Statement $3$: Some males are engineers.

We can draw the Venn diagram using the above statements.  Now, we can conclude from the above two Venn diagrams.

• Conclusion $\text{I}$: No engineer is a professor. ${\color{Red}{-\text{False}}}$
• Conclusion $\text{II}$: Some engineers are professors.${\color{Red}{-\text{False}}}$
• Conclusion $\text{III}$: No male is a teacher.${\color{Green}{-\text{True}}}$

Correct Answer $:\text{A}$

6.9k points 3 6 14

## Related questions

1 vote
Four girls $\text{P, Q, R and S}$ are studying languages in a University. $P$ is learning French and Dutch. $Q$ is learning Chinese and Japanese. $R$ is learning Spanish and French. $S$ is learning Dutch and Japanese. Given that: French is easier than Dutch; ... is easier than French. Based on the above information, which girl is learning the most difficult pair of languages? $P$ $Q$ $R$ $S$
Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$. $\text{Statement 1}:$ All entrepreneurs are wealthy. $\text{Statement 2}:$ All wealthy are risk seekers. $\text{Conclusion I}:$ ... $\text{I}$ nor $\text{II}$ is correct Both conclusions $\text{I}$ and $\text{II}$ are correct
Four cities $\text{P, Q, R}$ and $\text{S}$ are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of ... the minimum time required? $6$ hours $30$ minutes $3$ hours $45$ minutes $4$ hours $30$ minutes $5$ hours $15$ minutes
Fish belonging to species $S$ in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black pigment results in lower ... and disadvantages to species $S$ Having ultra-black skin is only disadvantageous to species $S$ but advantageous only to their predators
A $\text{CNC}$ worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is $5$ $\text{mm}$. The stepper motor completes one full revolution upon receiving $600$ pulses. If the worktable speed is $5$ m/minute and there is ... received by the stepper motor is $20$ $\text{kHz}$ $10$ $\text{kHz}$ $3$ $\text{kHz}$ $15$ $\text{kHz}$