Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All cards are boxes.
All boxes are torches.
All torches are shoes.
Conclusions:
I. All shoes are torches.
II. All torches are boxes.
III. All boxes are cards.
IV. All cards are shoes.
Option 1: Only conclusion IV follows
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: Only conclusion III follows
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Correct Answer: Only conclusion IV follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion
I:
All shoes are torches –
From the Venn diagram, it is evident that some parts of the circles representing shoes lie outside the circle representing torches while some lie inside. So, from this, it can be concluded that some shoes are torches. Therefore, this conclusion does not follow.
Conclusion
II:
All torches are boxes –
From the Venn diagram, it is evident that some parts of the circles representing torches lie outside the circle representing boxes while some lie inside. So, from this, it can be concluded that some torches are boxes. Therefore, this conclusion does not follow.
Conclusion III:
All boxes are cards –
From the Venn diagram, it is evident that some parts of the circles representing boxes lie outside the circle representing cards while some lie inside. So, from this, it can be concluded that some boxes are cards. Therefore, this conclusion does not follow.
Conclusion
IV:
All cards are shoes – From the Venn diagram, it is evident that the circle representing cards completely lies inside the circle representing shoes. So, from this, it can be concluded that all cards are shoes. Therefore, this conclusion follows.
So, only conclusion IV follows. Hence, the first option is correct.
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