Question

In each of the following questions, a statement is given followed by two conclusions I and II. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements.
Statements:
All students are boys.
No boys are dull.
Conclusion:
I. There are no girl students in the class.
II. No student is dull.
A. Only conclusion I is true.
B. Only conclusion II is true.
C. Both conclusions I and II are true.
D. Neither conclusion I nor conclusion II is true.

Answer 1

Hint: Here we use the given two statements and find the suitable conclusion which can be deduced from two statements.
* A conclusion is the result given on the basis of observations made.

Complete step-by-step solution:
All students are boys………….… (1)
No boys are dull……………….… (2)
From equation (1) we mean that all the students are boys (and there is no girl student)
From equation (2) we mean that none of the boys in the class is dull.
From equations (1) and (2), we can say that
\[ \Rightarrow \]All students are boys \[ + \]No boys are dull \[ = \]No student is dull in the class……………... … (3)
Now we check if the conclusions are true or not.
We have two conclusions:
I. There are no girl students in the class…………...… (4)
II. No student is dull……………..… (5)
From equation (4), conclusion I is only stating the facts about the first statement and does not state any fact about the second statement.
From equation (5), conclusion II states the result obtained from both the statements.
So, only conclusion II is true.
\[\therefore \]Both conclusion I and II are true

\[\therefore \]Correct option is option C.

Note: Students many times make the mistake of choosing the option stating both conclusions are true, which is wrong. Students think that the first conclusion is giving one of the results from statements but we should keep in mind that the statements are interlinked to each other, so the conclusion should contain results stating both statements.