If Pencils are Erasers, some Erasers are Sharpeners, some Erasers are Crayons, no Crayons are Sharpeners but some Crayons are Pencils then in the given Venn diagram, which of the following is represented by the shaded area?

Correct option is D

Given Information:

1. Pencils are Erasers: All Pencils are included in the set of Erasers.
2. Some Erasers are Sharpeners: There is an overlap between Erasers and Sharpeners.
3. Some Erasers are Crayons: There is an overlap between Erasers and Crayons.
4. No Crayons are Sharpeners: Crayons and Sharpeners do not overlap at all.
5. Some Crayons are Pencils: Crayons and Pencils overlap.

Understanding the Shaded Region:

The shaded region lies in the intersection of Pencils, Erasers, and Crayons, but it excludes Sharpeners (since Crayons and Sharpeners do not overlap).

Validation of Options:

• (a) Pencils and Sharpeners but not Erasers and Crayons:
  This is incorrect because the shaded region does not include Sharpeners, and Pencils are inherently part of Erasers.

• (b) Pencils and Erasers but not Sharpeners and Crayons:
  This is incorrect because the shaded region includes Crayons as well.

• (c) Pencils, Erasers, and Sharpeners but not Crayons:
  This is incorrect because Crayons are included in the shaded region, and Sharpeners are excluded.

• (d) Pencils, Erasers, and Crayons but not Sharpeners:
  This is correct because the shaded region represents the intersection of Pencils, Erasers, and Crayons, while excluding Sharpeners.

Final Answer:

S1. Ans. (d)
Sol. The shaded region represents the intersection of Pencils, Erasers, and Crayons, excluding Sharpeners.