Statements:
All plastic is waste
Some plastic is substance
Only a few metal is substance

Conclusions:
I. Some waste is substance
II. All metal being plastic is possibility

In each question below some statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Give answer-

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The correct option is If both conclusions I and II follow.

Step-by-Step Explanation:

1. Analyze the Statements:
- Statement 1: "All plastic is waste"
This means the set of all plastics is completely contained within the set of waste.
$\mathrm{Plastic}\subseteq \mathrm{Waste}$

- Statement 2: "Some plastic is substance"
This indicates a definite overlap between the set of plastic and the set of substance.
$\mathrm{Plastic}\cap \mathrm{Substance}\ne \varnothing$

- Statement 3: "Only a few metal is substance"
The phrase "Only a few" translates to a combination of "Some" and "Some not". This means:
- Some metal is substance ($\mathrm{Metal}\cap \mathrm{Substance}\ne \varnothing$)
- Some metal is NOT substance ($\mathrm{Metal}\cap {\mathrm{Substance}}^c\ne \varnothing$)

2. Evaluate Conclusion I: "Some waste is substance"
- From Statement 1, all plastics are inside waste.
- From Statement 2, some plastics are substances.
- Therefore, the portion of plastic that overlaps with substance also lies entirely within waste.
- This guarantees a definite overlap between waste and substance. Hence, Conclusion I logically follows.

3. Evaluate Conclusion II: "All metal being plastic is a possibility"
- We know that some metal is substance and some metal is not substance.
- Plastic has an overlap with substance, but plastic can also extend into regions that are not substance.
- There is no negative statement or restriction prohibiting metal from being contained within plastic.
- As long as the metal inside plastic preserves the condition that a portion of metal overlaps with substance and a portion does not, the diagram remains valid.
- Since a Venn diagram can be drawn where the entire circle of metal is inside the circle of plastic without contradicting any given statement, this condition is possible.
- Hence, Conclusion II logically follows as a possibility.

Conclusion:
Since both Conclusion I and Conclusion II logically follow from the given statements, the correct choice is If both conclusions I and II follow.