In the table, each cell with an "x" indicates that the body of water at the top of the column...

OWNING THE DATASET

Let's start by understanding what we're working with. We have a table showing which fish species are found in which bodies of water:

Fish Species	Swan Lake	Elbow Lake	Barb's Marsh	Lindsey Lake	Cedar Pond
Largemouth bass	X	X		X	X
Pumpkinseed	X	X	X		X
Yellow perch	X	X		X	X
Banded killifish		X
Black crappie		X
Brook stickleback			X
Central mudminnow			X
Northern redbelly dace			X
Northern pike				X

Key insights from our initial scan:

• Some species appear in multiple bodies of water (like Largemouth bass)
• Some species are unique to just one body of water (like Northern pike)
• No body of water contains all species
• Each body of water has at least one species

Understanding these patterns will help us answer the statements efficiently without checking every single combination.

ANALYZING STATEMENT 2 (Starting with the most efficient)

Statement 2 Translation:
Original: "No species of fish appears in all five bodies of water."
What we're looking for:

• Is there any species that has an "X" in all five columns?
• If no species appears in all five bodies, the statement is Yes

In other words: We're checking if any fish species is present everywhere.

To verify this statement, let's use visual pattern recognition. We need to see if any row has X's in all five columns.

Scanning each row quickly:

• Largemouth bass: Swan ✓, Elbow ✓, Barb's ✗, Lindsey ✓, Cedar ✓ (not in all)
• Pumpkinseed: Swan ✓, Elbow ✓, Barb's ✓, Lindsey ✗, Cedar ✓ (not in all)
• Yellow perch: Swan ✓, Elbow ✓, Barb's ✗, Lindsey ✓, Cedar ✓ (not in all)

We don't even need to check the remaining species since they appear in fewer locations than these first three. None of our species appears in all five bodies of water.

Statement 2 is Yes.

Teaching note: Notice how we didn't need to methodically count the X's for every species. Visual pattern recognition lets us quickly see that no row has all X's, and for the species that appear in multiple locations, we can quickly spot the missing X's.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "Each body of water contains at least one species of fish that appears in at least one other body of water."
What we're looking for:

• Does each body of water share at least one species with another body?
• If all bodies have at least one shared species, the statement is Yes

In other words: No body of water has only unique species.

Let's flip the logic to make this easier: If any body of water has ONLY unique species (species that don't appear elsewhere), then the statement would be No.

Let's check each body of water:

• Swan Lake: Contains Largemouth bass, Pumpkinseed, and Yellow perch - all appear in other bodies ✓
• Elbow Lake: Contains Largemouth bass, Pumpkinseed, Yellow perch (all shared), plus Banded killifish and Black crappie (unique) ✓
• Barb's Marsh: Contains Pumpkinseed (shared), plus Brook stickleback, Central mudminnow, and Northern redbelly dace (unique) ✓
• Lindsey Lake: Contains Largemouth bass and Yellow perch (shared), plus Northern pike (unique) ✓
• Cedar Pond: Contains Largemouth bass, Pumpkinseed, and Yellow perch - all appear in other bodies ✓

Every body of water contains at least one species that also appears in another body of water.

Statement 1 is Yes.

Teaching note: Instead of checking every species in every body of water, we focused on whether each body had at least one shared species. This is much faster than creating a complete inventory of which species are where.

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "It is possible to find a combination of exactly three bodies of water that, together, contain all nine species of fish."
What we're looking for:

• Can we find 3 bodies of water that collectively contain all 9 species?
• If such a combination exists, the statement is Yes

In other words: Is there a subset of exactly 3 locations that captures all species?

Rather than checking all possible combinations of three bodies of water (which would be time-consuming), let's be strategic.

First, let's identify bodies of water with unique species (species that appear nowhere else):

• Elbow Lake: Uniquely has Banded killifish and Black crappie
• Barb's Marsh: Uniquely has Brook stickleback, Central mudminnow, and Northern redbelly dace
• Lindsey Lake: Uniquely has Northern pike

These three bodies of water MUST be in our combination, otherwise we'd miss these unique species. Since we need exactly three bodies, these must be our answer.

Let's verify that Elbow Lake + Barb's Marsh + Lindsey Lake contains all species:

• From Elbow: Largemouth bass, Pumpkinseed, Yellow perch, Banded killifish, Black crappie
• From Barb's: Pumpkinseed, Brook stickleback, Central mudminnow, Northern redbelly dace
• From Lindsey: Largemouth bass, Yellow perch, Northern pike

Combined, they contain all 9 species!

Statement 3 is Yes.

Teaching note: By identifying the "must-include" bodies of water first (those with unique species), we eliminated the need to check multiple combinations. This constraint-based thinking is much more efficient than trying every possible grouping of three.

FINAL ANSWER COMPILATION

Statement 1: Yes
Statement 2: Yes
Statement 3: Yes

The correct answer is: Yes Yes Yes

LEARNING SUMMARY

Skills We Used

• Visual Pattern Recognition: For Statement 2, we quickly scanned for rows with all X's
• Strategic Constraint Identification: For Statement 3, we identified bodies with unique species that must be included
• Logical Reversal: For Statement 1, we flipped the question to "Does any body have ONLY unique species?"

Strategic Insights

• Solve statements in the most efficient order: We started with Statement 2 because it required a simple visual check, then moved to the more complex statements.
• Use constraints to eliminate options: When looking for combinations in Statement 3, we first identified bodies of water that must be included because they had unique species.
• Look for unique elements: Identifying which species appeared in only one location helped us solve Statement 3 instantly.
• When checking "all" conditions, find one counterexample: For Statement 2, we didn't need to check every species - just confirm none had all X's.

Common Mistakes We Avoided

• We didn't check every possible combination of three bodies of water for Statement 3
• We didn't create detailed lists of which species are in which locations when not needed
• We avoided checking all species for Statement 2 after seeing that even the most widespread didn't appear everywhere

This problem teaches us that in table analysis questions, visual pattern recognition and strategic thinking about constraints can dramatically reduce the work needed to find the answer.