Question

If Lewis participated in two sports, which of the following is definitely false?

• A. Mike did not participate in Skiing.
• B. John participated in Paragliding.
• C. Lewis participated in Skiing.
• D. Mike participated in Paragliding.

Hint:

Always map individuals to sets using constraints and eliminate contradictions when validating definite statements.

Answer 1

The Correct Option is B

Let’s analyze step-by-step: From statement (i): Rock Climbing (RC) = \(x\)
Paragliding (PG) = \(2x\)
Bungee Jumping (BJ) = \(2x\)
Skiing (SK) = \(2x + 1\)
This implies a total of: \[ x + 2x + 2x + (2x + 1) = 7x + 1 \] Since 4 people must take part in at least one event and each event has at least one participant, choose \(x = 1\) \(\Rightarrow\) RC = 1, PG = 2, BJ = 2, SK = 3 From (iii):
- John: Skiing but not Rock Climbing; not Paragliding
- Lewis: Bungee Jumping but not Paragliding
From (vi): Mike did exactly one among Skiing and Paragliding
From (ii): Each person did at least one event.
From (iv): No person did both BJ and RC.
From (v): Peter did three events.
Suppose Lewis did Skiing and BJ (2 sports). That satisfies (iii).
Check if John can do Paragliding:
(iii) says he did **not** do Paragliding. So if option
(b) says “John participated in Paragliding” → it contradicts the premise. Final Answer: \( \boxed{\text{B}} \)