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In each question below are given three statements followed by four conclusions numbered I, II, III and IV. You have to take the three given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the three given statements, disregarding commonly known facts.
Statements: All pens are pencils. Some pens are erasers. Some erasers are clips.
Conclusions:
I. Some clips are pens.
II. No clip is a pen.
III. Some erasers are pencils.
IV. No eraser is a pencil.
We know: All pens are pencils. Some pens are erasers. Some erasers are clips.
We shall now test each of the conclusions and try negating them. The ones that will be necessarily true in every case shall be valid in nature.
1 and 2. Some clips are pens, and no clip is a pen: We know that some pens are erasers and some erasers are in-turn clips. Hence, clips and pens can overlap, or they can be disjointed sets. There is no other possibility. Hence, either of 1 or 2 shall be true.
3. Some erasers are pencils: We know that all pens are pencils, and some pens are erasers. Hence, there are definitely some pens that are both erasers and pencils, making at least a small part of erasers overlap with pencils. This makes 3 a valid conclusion.
4. No eraser is a pencil: This is an invalid conclusion as there are definitely some pens that are both erasers and pencils, making at least a small part of erasers overlap with pencils.
