June birthday with tight overlap: Rajat remembers his mother's birthday is not after 18 June (i.e., ≤ 18). His sister remembers it is before 20 June but after 17 June (i.e., only 18). On which date was the birthday?

Introduction / Context:
This is another set-intersection task but with one clue explicitly capping the latest possible date. Combining a “not after” cap with a tight two-day window can yield a single value.

Given Data / Assumptions:

• Rajat: “not after 18 June” ⇒ {… , 18}. Within plausible days, {17, 18} might both be possible from this statement alone.
• Sister: “before 20 but after 17” ⇒ {18, 19}.

Concept / Approach:
Intersect Rajat’s cap with the sister’s two-day window.

Step-by-Step Solution:

Verification / Alternative check:
Even if you misread “not after 18” as “on or before 18,” the conclusion stays {18} once intersected with {18, 19}.

Why Other Options Are Wrong:

• 17th: Excluded by sister’s “after 17.”
• 19th: Excluded by Rajat’s “not after 18.”
• “17th or 18th”: Overstates uncertainty; data narrow it to only 18th.

Common Pitfalls:
Confusing “not after” with “after not,” or swapping inclusivity of endpoints.

Final Answer:
18th