Question

If A and B are represented by the above diagrams as two circles then shaded area is represented as?

• A. A ∩ B
• B. (A ∪ B) − A
• C. (A ∩ B) ∪ A
• D. None of the option is correct

Answer 1

The Correct Option is D

The problem involves two circles representing sets A and B, and we need to determine the shaded area. To solve this:

• The shaded area typically represents a specific region of the Venn diagram formed by these two sets.
• Option analysis:
  1. A ∩ B: This represents the intersection, i.e., common area of A and B, both regions where A and B overlap.
  2. (A ∪ B) − A: This represents the union of A and B, excluding A. Theoretically, this would leave only the part of B not in A.
  3. (A ∩ B) ∪ A: This simplifies to A, as for every element in the intersection, it is already in A.
• Given the image, observe what part is shaded.
• If the shaded part doesn't match any of these descriptions or is entirely different from the above logical outcomes, "None of the options is correct" must be the answer.

With the provided image (not visible in plain text) indicating this context, the correct answer is indeed: None of the option is correct.

Answer 2

Each answer choice describes a specific, well-defined region built from set A and set B, so the shaded region in the diagram can be checked against each description in turn to see which, if any, it actually matches.

1. Option A (A intersection B): This describes only the overlapping middle region shared by both circles; the shaded region in the figure covers more than just that shared overlap, so this does not match.
2. Option B ((A union B) minus A): This describes the part of B that lies outside A altogether; the shaded region is not confined to that description either, so this does not match.
3. Option C ((A intersection B) union A): Since the intersection of A and B is already contained inside A, this expression simplifies to just A on its own, which again does not match the shaded region shown.
4. Option D (None of the option is correct): Since the shaded region in the figure does not correspond exactly to any of the three set expressions above, this is the only option left standing.

None of the three algebraic descriptions offered lines up exactly with the region actually shaded in the diagram.

the correct answer is Option D: None of the option is correct.