Question

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

Statements:

All drawers are racks.

Some racks are cabinets.

All cabinets are shelves.

Conclusions:

(1) All shelves are racks.

(11) Some shelves are drawers.

• A. Neither conclusion (1) nor (Il) follows
• B. Only conclusion (1) follows
• C. Both conclusions (1) and (II) follow
• D. Only conclusion (I1) follows

Answer 1

Answer:

A. Neither conclusion (1) nor (Il) follows

Let’s translate the statements into logical relations:

Statements:

1. All drawers are racks → Drawers ⊆ Racks

2. Some racks are cabinets → Some Racks ∩ Cabinets

3. All cabinets are shelves → Cabinets ⊆ Shelves

   Conclusion (1): All shelves are racks

• We only know: Cabinets ⊆ Shelves and some Racks are Cabinets

• But nothing says all shelves are racks
  Does NOT follow

  Conclusion (2): Some shelves are drawers

• Drawers ⊆ Racks

• Some Racks are Cabinets, and Cabinets ⊆ Shelves

• But there is no direct link that drawers overlap with cabinets/shelves
  Does NOT follow

  Final Answer:

Neither (1) nor (2) follows