Pradeep correctly remembers that his mother's birthday is before the twenty third of February but after the nineteenth of February. His brother correctly remembers that their mother's birthday is not on or after the twenty second of February. On which day in February is their mother's birthday definitely?

Introduction / Context:
This logical reasoning question concerns date constraints and overlapping ranges. Two brothers, Pradeep and his sibling, recall different but consistent information about their mother's birthday in February. We must combine both pieces of information to find which particular date or dates are definitely possible and then choose the option that best reflects the conclusion.

Given Data / Assumptions:

• All dates are in February of the same year.
• Pradeep remembers that his mother's birthday is before the twenty third of February but after the nineteenth of February.
• His brother remembers that their mother's birthday is not on or after the twenty second of February.
• We assume both memories are correct.
• We must decide which date or dates are consistent with both memories.

Concept / Approach:
The key idea is to translate verbal expressions about dates into inequalities and then find the intersection of the resulting ranges. Phrases like before the twenty third and after the nineteenth must be interpreted strictly. Similarly, not on or after the twenty second defines an upper bound for the birthday. The intersection of these constraints yields all possible dates that satisfy both brothers' memories. The answer choice must then match that set of dates as closely as possible.

Step-by-Step Solution:
Step 1: From Pradeep's memory, the birthday is before the twenty third of February and after the nineteenth of February. Step 2: After the nineteenth means later than the nineteenth, so the birthday is on the twentieth, twenty first or twenty second of February. Step 3: Before the twenty third means earlier than the twenty third, which still allows the twentieth, twenty first and twenty second. So from Pradeep alone, the possible dates are 20, 21 and 22 February. Step 4: Now consider the brother's memory: the birthday is not on or after the twenty second of February. Step 5: Not on or after the twenty second means that the birthday is strictly earlier than the twenty second. So from this statement, possible dates are any in February that are less than 22, that is, first through twenty first. Step 6: We must assume both memories are correct, so the actual birthday must satisfy both constraints at the same time. Step 7: From Pradeep's memory, the birthday is in the set {20, 21, 22}. From the brother's memory, it is in the set {1, 2, ..., 21}. The intersection of these sets contains dates that are in both sets. Step 8: The intersection is {20, 21}. So the birthday must be either 20 February or 21 February. Step 9: We cannot decide between 20 and 21 uniquely. Both dates are consistent with both statements, so both remain possible.

Verification / Alternative check:
Check date 20 February: It is after the nineteenth and before the twenty third, so it matches Pradeep's memory. It is also before the twenty second, so it matches the brother's memory. Check date 21 February: It is again after the nineteenth and before the twenty third, and it is still before the twenty second, so it satisfies both memories. Check date 22 February: It fits Pradeep's condition of being after the nineteenth and before the twenty third but violates the brother's condition, because the brother says the birthday is not on or after the twenty second. Therefore 22 February is not possible.

Why Other Options Are Wrong:
Option b (20 February) is wrong because 21 February is also a valid possibility; the day is not uniquely fixed. Option c (21 February) is similarly wrong because 20 February also fits all constraints. Option d (None of these) is wrong because the set 20 or 21 February exactly matches the range of valid dates.

Common Pitfalls:
One common mistake is to misread the phrase not on or after the twenty second as not after the twenty second, which would still allow the birthday to be on the twenty second. However, the wording clearly excludes both on the twenty second and any later date. Another mistake is to think that the word definitely means that a single unique date must be selected. In fact, sometimes the most precise answer is a small set of possible dates, and in this question the option 20 or 21 February correctly represents that set. Careful reading and precise translation to inequalities are essential.

Final Answer:
Their mother's birthday must be either on 20 February or on 21 February. Correct option: 20 or 21 February.