Question : Directions: Three statements are followed by three conclusions numbered I, II, and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follows (s) from the given statements.
Statements:
All tools are spanners.
Some spanners are utensils.
No spanner is an iron.
Conclusions:
(I) Some tools are irons.
(II) Some utensils are tools.
(III) Some utensils are not iron.
Option 1: Only conclusion III follows
Option 2: All conclusions I, II, and III follow
Option 3: Only conclusion I follows
Option 4: Either conclusion I or conclusion III follows
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Correct Answer: Only conclusion III follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some tools are irons – From the Venn diagram, it is evident that there is a negative relation between spanners and irons and all tools are spanners. So, from this, it can be concluded that no tool is a spanner. Thus, this conclusion does not follow.
Conclusion (II):
Some utensils are tools – From the Venn diagram, it is evident that there is no direct relation between tools and utensils. So, no definite relation can be drawn. Thus, this conclusion doesn't follow.
Conclusion (III):
Some utensils are not iron – From the Venn diagram, it is evident that no spanner is iron. So, the part of the circle representing utensils that lie inside the circle representing spanners cannot be iron. Therefore, it can be concluded that some utensils are not iron.
Therefore, only conclusion III follows. Hence, the first option is correct.
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