Date narrowing – Meeta remembers her father's birthday is after 8 July but before 12 July. Her brother remembers it is after 10 July but before 15 July. On which day in July is the birthday definitely?

Introduction / Context:
We are intersecting two open intervals described in words. One memory gives (8, 12), the other gives (10, 15). The definite day is their intersection.

Given Data / Assumptions:

• After 8 July but before 12 July → possible dates: 9, 10, 11.
• After 10 July but before 15 July → possible dates: 11, 12, 13, 14.

Concept / Approach:
Compute the set intersection of the two candidate sets.

Step-by-Step Solution:

Verification / Alternative check:
Check boundary words carefully: “after” excludes the boundary day; “before” also excludes the boundary. That is why 8 and 12 are excluded from Meeta's set, and 10 and 15 from the brother's set.

Why Other Options Are Wrong:

• 10th: Not in the brother's range.
• 10th or 11th / Can't be determined: Intersection is a single value (11).
• 12th: Not in Meeta's range.

Common Pitfalls:
Including endpoints despite the word “after/before”; treating “between” inclusive. Read quantifiers precisely.

Final Answer:
11th