Question : Directions: Two statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All coffees and milkshakes are teas.
None of the coffees are milkshakes.
Conclusions:
I. Some coffees are milkshakes.
II. Some teas are coffees.
III. Some milkshakes are teas.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I and II follow
Option 3: Only conclusions I and III follow
Option 4: All of the conclusions follow
Correct Answer: Only conclusions II and III follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some coffees are milkshakes – From the Venn diagram, it is evident that there is a negative relation between coffee and milkshakes. So, this conclusion does not follow.
Conclusion (II):
Some teas are coffees – From the Venn diagram, it is evident that some parts of the circle representing teas lie outside the circle representing coffee while some lie inside. So, it can be concluded that some teas are coffees. Thus, this conclusion follows.
Conclusion (III):
Some milkshakes are teas – From the Venn diagram, it is evident that the circle representing milkshakes completely lies inside the circle representing teas. Since all milkshakes are teas, some milkshakes will definitely be teas. Thus, this conclusion follows.
So, the only conclusions II and III follow. Hence, the first option is correct.
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