Logical Deductions

What are Logical Deductions?

These questions give you a set of statements and ask you to draw a valid conclusion. Only use what the statements tell you — do not add outside assumptions.

All / Some / No Statements

• All A are B → Every single A is also a B
• Some A are B → At least one A is a B (but not necessarily all)
• No A are B → Not a single A is a B

Example:
"All dogs are animals. Some animals are pets. Can we conclude all dogs are pets?"
→ No — some animals are pets, but we cannot guarantee dogs are among those pets.

If-Then & Ordering Deductions

If-Then Statements

If P then Q: whenever P is true, Q must also be true.

Watch out for the common trap:
"If it rains, the ground is wet. The ground is wet. Did it rain?"
→ Not necessarily — the ground could be wet for another reason.

Ordering / Ranking Deductions

Arrange items from clues.

Example: Alice is taller than Bob. Bob is taller than Clare. Sam is shorter than Clare.
Order tallest to shortest: Alice > Bob > Clare > Sam

Strategy & Key Tips

1. List each statement clearly.
2. Draw a simple diagram — Venn diagram for All/Some, number line for ordering.
3. Only conclude what is definitely true, not just possible.

Key Tips

• "All A are B" does NOT mean "All B are A" — direction matters
• Draw Venn diagrams for All/Some/No problems — they make the logic visual
• For ordering, use a number line or ranked list to avoid errors
• Eliminate answer choices that require assumptions not given in the statements