Question : Directions: Three statements are 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 conclusions logically follow(s) from the statements.
Statements:
I. All metals are gold.
II. All jewellery is gold.
III. All gold are ornaments.
Conclusions:
I. Some ornaments are jewellery.
II. Some metals are jewellery.
III. All jewellery are ornaments.
Option 1: Only conclusions I and III follow
Option 2: All conclusions follow
Option 3: Only conclusions II and III follow
Option 4: Only conclusions I and II follow
Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
Some ornaments are jewellery – From the Venn diagram, it is clear that only some part of the circle of ornament lies inside the circle of jewellery. Therefore, this conclusion is true.
Conclusion II:
Some metals are jewellery – From the Venn diagram, it is clear that there is no direct relation between metals and jewellery. Therefore, this conclusion does not follow.
Conclusion (III):
All jewellery is ornaments – From the Venn diagram, it is clear that the circle of jewellery is completely inside the circle of ornaments. Therefore, this conclusion follows.
Therefore, only conclusions I and III follow. Hence, the first option is correct.
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