The Megac Corporation has an ownership stake in the Sysinc Corporation. The Exino Corporation has an ownership stake in the...

Solution: Ownership Structure Analysis

Visual Representation of Ownership Structure

Direct Ownership Relationships (as stated):

• \(\mathrm{Megac} \rightarrow \mathrm{Sysinc}\)
• \(\mathrm{Exino} \rightarrow \mathrm{Naturo}\)
• \(\mathrm{Green\ Valley} \rightarrow \mathrm{Exino}\)
• \(\mathrm{Jenyx} \rightarrow \mathrm{Green\ Valley}\)
• \(\mathrm{Sysinc} \rightarrow \mathrm{Green\ Valley}\)

Complete Ownership Map (including transitive ownership):

Applying the transitivity rule systematically:

Megac owns:

• Sysinc (direct)
• Green Valley (through Sysinc)
• Exino (through \(\mathrm{Sysinc} \rightarrow \mathrm{Green\ Valley}\))
• Naturo (through \(\mathrm{Sysinc} \rightarrow \mathrm{Green\ Valley} \rightarrow \mathrm{Exino}\))

Jenyx owns:

• Green Valley (direct)
• Exino (through Green Valley)
• Naturo (through \(\mathrm{Green\ Valley} \rightarrow \mathrm{Exino}\))

Sysinc owns:

• Green Valley (direct)
• Exino (through Green Valley)
• Naturo (through \(\mathrm{Green\ Valley} \rightarrow \mathrm{Exino}\))

Green Valley owns:

• Exino (direct)
• Naturo (through Exino)

Exino owns:

• Naturo (direct)

Understanding the Question

We need to find corporations that:

1. Megac could acquire a first-time ownership stake in
2. Jenyx could acquire a first-time ownership stake in

Critical Insight: Anti-Circularity Constraint

The key constraint states: "if Corporation A has an ownership stake in Corporation B, then Corporation B cannot have an ownership stake in Corporation A."

This means:

• If there's any ownership path from A to B, then B cannot own A
• This prevents circular ownership structures

Strategic Analysis

For Megac:

• Currently owns: Sysinc, Green Valley, Exino, Naturo
• From answer choices, doesn't own: Jenyx
• Can Megac acquire Jenyx? Check if this would violate anti-circularity:
• There's no ownership path from Jenyx to Megac
• Therefore, Megac can acquire Jenyx ✓

For Jenyx:

• Currently owns: Green Valley, Exino, Naturo
• From answer choices, doesn't own: Megac
• Can Jenyx acquire Megac? Check if this would violate anti-circularity:
• There's no ownership path from Megac to Jenyx
• Therefore, Jenyx can acquire Megac ✓

Verification Through Logic

Why these acquisitions are valid:

• Megac acquiring Jenyx: Creates \(\mathrm{Megac} \rightarrow \mathrm{Jenyx} \rightarrow \mathrm{Green\ Valley}\), but Megac already owns Green Valley through Sysinc. No cycle created.
• Jenyx acquiring Megac: Creates \(\mathrm{Jenyx} \rightarrow \mathrm{Megac} \rightarrow \mathrm{Sysinc} \rightarrow \mathrm{Green\ Valley}\), but Jenyx already owns Green Valley directly. No cycle created.

Final Solution Synthesis

Step-by-step recap:

1. Mapped all ownership relationships using transitivity
2. Identified which corporations each entity currently owns
3. Found corporations available for first-time acquisition
4. Verified no anti-circularity violations would occur

Final Answer:

• Megac column: Jenyx
• Jenyx column: Megac

Key Insight: The anti-circularity rule prevents ownership loops but allows multiple paths to the same corporation. Both proposed acquisitions create additional paths to already-owned corporations without creating prohibited cycles.

Exam Strategy: In ownership/hierarchy problems, always map the complete transitive closure first, then check constraints systematically rather than testing combinations randomly.