Question:
If John participated in Paragliding, which of the following statements is definitely true?
If John participated in Paragliding, which of the following statements is definitely true?
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Use logical contradiction chains to eliminate and confirm possible mappings. Always test against all known constraints.
Updated On: Jul 28, 2025
- Mike participated in Rock Climbing.
- John participated in Bungee Jumping.
- Lewis did not participate in Skiing.
- Peter did not participate in Rock Climbing.
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The Correct Option is A
Solution and Explanation
Statement (iii) says:
John participated in Skiing but not in Rock Climbing, and not in Paragliding.
If now John is participating in Paragliding, then this contradicts the earlier info.
So we now temporarily assume (hypothetically) that John is in PG, and see what follows.
From (vi): Mike participated in exactly one of Skiing and Paragliding. If John is in PG, and we know Lewis is not in PG (from iii), then among John and Lewis, PG is partially filled.
Since only two people can be in PG (PG = 2x = 2), the other must be Mike.
Therefore, Mike is in PG.
But this contradicts (vi), which said Mike is in only one of Skiing and PG.
So Mike is not in PG \(\Rightarrow\) Mike must be in Skiing.
Then Peter must be the other person in PG (to fulfill PG = 2 people).
Now: Mike is in Skiing, not in PG.
So Mike must be in Rock Climbing (to fulfill event participation constraint), because he must do at least one sport and not both PG and Skiing.
But he already did Skiing, so he must not do PG \(\Rightarrow\) Rock Climbing is the only other event.
So (A) Mike participated in Rock Climbing is necessarily true. \[ \Rightarrow \boxed{\text{A}} \]
From (vi): Mike participated in exactly one of Skiing and Paragliding. If John is in PG, and we know Lewis is not in PG (from iii), then among John and Lewis, PG is partially filled.
Since only two people can be in PG (PG = 2x = 2), the other must be Mike.
Therefore, Mike is in PG.
But this contradicts (vi), which said Mike is in only one of Skiing and PG.
So Mike is not in PG \(\Rightarrow\) Mike must be in Skiing.
Then Peter must be the other person in PG (to fulfill PG = 2 people).
Now: Mike is in Skiing, not in PG.
So Mike must be in Rock Climbing (to fulfill event participation constraint), because he must do at least one sport and not both PG and Skiing.
But he already did Skiing, so he must not do PG \(\Rightarrow\) Rock Climbing is the only other event.
So (A) Mike participated in Rock Climbing is necessarily true. \[ \Rightarrow \boxed{\text{A}} \]
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