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FL – Must Be True Cheat Sheet - Coggle Diagram
FL – Must Be True Cheat Sheet
✅ 1. Identify the Conditional Statements
Look for clues:
"If... then..."
"Only if..."
"Unless..."
"All / Every / Any / Each..."
"No / None..."
"Requires / Depends / Necessitates..."
Write them symbolically:
"If A, then B" → A → B
"Only if C, then D" → D → C
🔄 2. Take the Contrapositive
For every A → B, also write:
~B → ~A
This gives you another valid inference path.
🔗 3. Look for Chains
If you have:
A → B
B → C
Then you can link them:
→ A → C
🚫 4. Avoid These Trap Mistakes
❌ Mistaken reversal: A → B → You cannot say B → A
❌ Mistaken negation: A → B → You cannot say ~A → ~B
📌 5. Pick the Choice That Must Be True
Valid answer types:
A properly derived chain (A → C)
A valid contrapositive
Something logically contained in all paths
🧪 6.Quantifier & Trigger Translation
All / Universal (Sufficient)
All → A → B
Every → A → B
Each → A → B
Any → A → B
If → A → B
People who → A → B
In order to → A → B
Whenever → A → B
Some / Existential (Reversible)
Some → A ∃ B ⇄ B ∃ A
Many → A ∃ B ⇄ B ∃ A
Several → A ∃ B ⇄ B ∃ A
A few → A ∃ B ⇄ B ∃ A
At least one → A ∃ B ⇄ B ∃ A
There is / are → A ∃ B ⇄ B ∃ A
None / Negated Universal
No → A → ~B
None → A → ~B
Never → A → ~B
Not All / Negated Existential
Not all → Some A → ~B