Question : Directions: Consider the given statement(s) to be true and decide which of the given conclusions can be drawn from the given statement.
Statements:
All cycles are ducks.
All ducks are swans.
Conclusions:
I. All swans are cycles.
II. Some swans are cycles.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusion I and conclusion II follow
Option 4: Neither Conclusion I nor Conclusion II follows
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Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All swans are cycles – From the Venn diagram, it is evident that some parts of the circle representing swans lie outside the circle representing cycles while some lie inside. So, from this, it can be concluded that some swans are cycles. Therefore, this conclusion does not follow.
Conclusion (II):
Some swans are cycles – From the Venn diagram, it is evident that some parts of the circle representing swans lie outside the circle representing cycles while some lie inside. So, from this, it can be concluded that some swans are cycles. Therefore, this conclusion follows.
Therefore, only the conclusion II follows. Hence, the second option is correct.
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