Finding Deepak's Birthday: A Logic Puzzle

This question is a classic logic puzzle where we need to find a specific date based on overlapping information provided by two different people, Kailash and Geeta, about Deepak's birthday in May.

Analyzing Kailash's Statement about Deepak's Birthday

Kailash remembers that Deepak's birthday falls after the 20^th of May but before the 28^th of May.

This means the possible dates for Deepak's birthday, according to Kailash, are:

• 21^st May
• 22^nd May
• 23^rd May
• 24^th May
• 25^th May
• 26^th May
• 27^th May

We can represent this set of dates as: ${Kailash} = \{21, 22, 23, 24, 25, 26, 27\}$.

Analyzing Geeta's Statement about Deepak's Birthday

Geeta remembers that Deepak's birthday falls before the 22^nd of May but after the 12^th of May.

This means the possible dates for Deepak's birthday, according to Geeta, are:

• 13^th May
• 14^th May
• 15^th May
• 16^th May
• 17^th May
• 18^th May
• 19^th May
• 20^th May
• 21^st May

We can represent this set of dates as: ${Geeta} = \{13, 14, 15, 16, 17, 18, 19, 20, 21\}$.

Finding the Intersection: The Common Date

Deepak's birthday must satisfy both Kailash's and Geeta's conditions. Therefore, the actual date must be present in both sets of possible dates.

We need to find the intersection of the two sets: ${Kailash} \cap {Geeta}$.

Comparing the two lists:

• Kailash's possible dates: 21, 22, 23, 24, 25, 26, 27
• Geeta's possible dates: 13, 14, 15, 16, 17, 18, 19, 20, 21

The only date that appears in both lists is the 21^st of May.

So, the intersection is ${Kailash} \cap {Geeta} = \{21\}$.

Conclusion on Deepak's Birthday

Based on the information provided by both Kailash and Geeta, the only possible date for Deepak's birthday is the 21^st of May.

Therefore, Deepak's birthday falls on the 21^st of May.

Revision Table: Key Logic Concepts

Additional Information: Solving Date-Based Reasoning

Date-based reasoning problems often involve combining different pieces of information to narrow down a range of possibilities to a single answer. Here are some tips:

• Always list out the possible dates based on each piece of information separately.
• Pay close attention to words like "after", "before", "inclusive", and "exclusive". "After 20^th" means 21^st is the earliest, while "before 22^nd" means 21^st is the latest.
• Visualizing the dates on a timeline can be helpful, although not strictly necessary for simpler problems like this one.
• The final answer must be the date(s) that fit all the given conditions simultaneously. This is the intersection of all individual sets of possibilities.

This type of problem tests your ability to follow instructions carefully and identify the overlap between different constraints to deduce the correct answer.