Question

Jim. George, and Sue belong to an outdoor club. Every club member is either a skier or a mountain climber, but no member is both. No mountain climber likes rain, and all skiers like snow. George dislikes whatever Jim likes and likes whatever Sue dislikes. Jim and Sue both like rain and snow. Is there a member of the outdoor club who is a mountain climber?

Short answer

Yes, George is a mountain climber.

Step-by-step solution

Understanding the Problem

We need to determine if there is a mountain climber in the outdoor club comprising Jim, George, and Sue. Each member is either a skier or a mountain climber, but not both. Mountain climbers dislike rain, while skiers like snow. Assess the preferences and dislikes of Jim, George, and Sue to find if any member is a mountain climber.

Analyzing Individual Preferences

According to the problem, Jim and Sue both like rain and snow. Since mountain climbers dislike rain, neither Jim nor Sue can be mountain climbers. They must both be skiers since skiers like snow, which aligns with their preferences.

Examining George's Preferences

George dislikes what Jim likes and likes what Sue dislikes. Since Jim likes rain and snow, George must dislike both rain and snow. Georgia liking the opposite of Sue, if Sue likes rain and snow, implies George dislikes rain and snow. This aversion to snow means George cannot be a skier (as skiers like snow).

Determining George's Club Role

As skiers like snow and George does not, George cannot be a skier. Conversely, since mountain climbers dislike rain and George dislikes rain as well, George fits the profile of a mountain climber. Thus, George is a mountain climber.

Key concepts

Logic Puzzles

Logic puzzles involve using reasoning skills to solve problems by setting up possibilities and eliminating inconsistencies. In our exercise with Jim, George, and Sue, we needed to deduce the role of each club member as either a skier or a mountain climber. To solve logic puzzles efficiently, follow these steps:

• Identify all given information and note it down clearly.
• Understand the constraints and relationships within this information.
• Use the process of elimination to narrow down possibilities.
• Confirm conclusions by ensuring all constraints are satisfied.

This approach allows us to handle the complexities posed by intertwining clues. In the example, Jim and Sue's liking of rain and snow clearly ruled out the possibility of them being mountain climbers, leading us to deduce their roles as skiers. Simultaneously, George's contrasting preferences ultimately affirmed him as the mountain climber.

Problem Solving

Problem solving is a systematic approach to finding solutions to complex questions. It involves understanding what is being asked, analyzing the information provided, devising a plan, carrying it out, and evaluating the outcome. Here's how we applied problem-solving strategies to our logic puzzle:

• Understand the Problem: Determine what exactly is being asked - in this case, establishing if any member is a mountain climber.
• Gather Information: Identify the preferences and dislikes of each character within the context of the problem.
• Analyze and Plan: Consider each member's likes and dislikes in relation to the definition of a skier and a mountain climber.
• Execute the Plan: Step through each character's traits logically to eliminate impossible scenarios.
• Evaluate: Check that the solution correctly meets all constraints given in the problem.

By following a problem-solving framework, complex scenarios become manageable, allowing a systematic breakdown until you arrive at a solution.

Set Theory

Set theory is a branch of mathematics that deals with the study of collections of objects, known as sets. In our exercise, it provides a more structured way to view the preferences and roles of Jim, George, and Sue. Here's how we can interpret the problem using set theory concepts:

• We can define two sets: \( S \) as the set of skiers who like snow and \( M \) as the set of mountain climbers who dislike rain.
• It's given that each member belongs either to \( S \) or \( M \), but not both. Therefore, \( S \cup M \) contains all club members, and \( S \cap M = \emptyset \).
• Jim and Sue both like rain and snow, establishing them as members of set \( S \) (skiers).
• George, who dislikes what Jim likes (rain and snow), cannot belong to set \( S \), therefore, he must be in set \( M \) (mountain climbers).

Set theory helps clarify the structure of problems and can make it easier to determine relationships and frameworks, pushing towards the right solution. Each club member's traits or elements fall distinctly into one set or another, leaving no room for overlap.