Module Complete
Translation — Quick Reference
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Completion
Translation Patterns
| Symbol | Name | Truth Condition |
|---|---|---|
| if P then Q | Implication | P → Q |
| P only if Q | Necessary Condition | P → Q |
| P if Q | Sufficient Condition | Q → P |
| unless P | If not | ¬P → ... |
| neither...nor | Both false | ¬A ∧ ¬B |
Tricky Patterns
Only if ≠ If
"A only if B" = A → B (B necessary)
"A if B" = B → A (B sufficient)
Unless = If not
"A unless B" = ¬B → A
Key Takeaways
1
"Only if" creates forward implication
2
"Unless" means "if not"
3
"Neither...nor" = both negated with AND
4
When ambiguous, ask for clarification
5
Assume inclusive OR unless stated otherwise
⊢→
Up Next
Module 3: Validity & Proofs
Constructing and verifying logical arguments