Birthday inference from overlapping memory windows: Meena correctly remembers that her father's birthday falls after 18 May but before 22 May (i.e., one of 19, 20, or 21). Her brother correctly remembers that their father's birthday is before 24 May but after 20 May (i.e., one of 21, 22, or 23). On which exact date in May was their father's birthday?

Introduction / Context:
Many ranking and date-overlap problems in verbal reasoning ask you to combine two incomplete but correct memories to pinpoint a single day. The key skill is to translate each statement into a precise set of candidate dates and then take the intersection. This mirrors set-intersection logic used in data filtering and calendar constraints.

Given Data / Assumptions:

• Meena: “after 18 May but before 22 May” ⇒ {19, 20, 21}.
• Brother: “before 24 May but after 20 May” ⇒ {21, 22, 23}.
• All dates are in May of the same year; no leap-year or calendar irregularities matter.

Concept / Approach:
The approach is set intersection. Convert each natural-language window into a closed or open range. Then take the overlap (common elements). If that overlap is a single date, the answer is definite; if multiple, the answer is “Cannot be determined.”

Step-by-Step Solution:

Verification / Alternative check:
If the brother’s window had been “on or after 21 May and on or before 23 May,” the set would remain {21, 22, 23} and the intersection would still be {21}. Any slight widening that includes 20 or narrows to remove 21 would change the conclusion; here it does not.

Why Other Options Are Wrong:

• 19th May: Not in the brother’s set.
• 20th May: Not in the brother’s set.
• 18th May: Excluded by Meena’s “after 18 May.”
• Cannot be determined: The intersection is a single date, so we can determine it.

Common Pitfalls:
Forgetting that “after” and “before” are strict (exclude the endpoints). Including 18 or 22 by mistake changes the sets and leads to wrong intersections. Always write the candidate sets explicitly before intersecting.

Final Answer:
21st May