Question : Directions: Three 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:
I. All pencils are colours.
II. All colours are paints.
III. Some paints are drawings.
Conclusions:
I. Some pencils are drawings.
II. Some paints are colours.
III. Some colours are pencils.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: All 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 pencils are drawings – From the Venn diagram, there is no direct relation between pencils and drawings. Therefore, this conclusion does not follow.
Conclusion (II):
Some paints are colours – From the Venn diagram, it is clear that some part of the circle representing paints lies outside the circle representing colours whereas some lie inside. Therefore, this conclusion follows.
Conclusion (III):
Some colours are pencils – From the Venn diagram, it is clear that some part of the circle representing colours lies outside the circle representing pencils whereas some lie inside. Therefore, this conclusion follows.
So, only conclusions II and III follow. Hence, the second option is correct.
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