vx((DxHx) → (Ox v Ux)) : Everything in my dreams that has horns is either an owl or a human being. (a) Good Translation (b) Bad Translation Submit

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Logical Formulation and Translation Evaluation**

**Statement:**
∀x((Dx ∧ Hx) → (Ox ∨ Ux)) : Everything in my dreams that has horns is either an owl or a human being.

**Translation Evaluation:**

- **Option (a):** Good Translation
- **Option (b):** Bad Translation *(Selected)*

**Explanation:**

The logical expression uses universal quantification (∀x) to state that for every element x, if x exists in "my dreams" (Dx) and has "horns" (Hx), then x is either "an owl" (Ox) or "a human being" (Ux).

The choice marked is *(b) Bad Translation*, indicating the provided English translation is considered incorrect according to the logical statement structure. 

**Considerations:**

- Check the structure of the logical expression against the natural language translation for accuracy.
- Assess the completeness and correctness of interpreting logical operators and quantifiers in translations.
Transcribed Image Text:**Logical Formulation and Translation Evaluation** **Statement:** ∀x((Dx ∧ Hx) → (Ox ∨ Ux)) : Everything in my dreams that has horns is either an owl or a human being. **Translation Evaluation:** - **Option (a):** Good Translation - **Option (b):** Bad Translation *(Selected)* **Explanation:** The logical expression uses universal quantification (∀x) to state that for every element x, if x exists in "my dreams" (Dx) and has "horns" (Hx), then x is either "an owl" (Ox) or "a human being" (Ux). The choice marked is *(b) Bad Translation*, indicating the provided English translation is considered incorrect according to the logical statement structure. **Considerations:** - Check the structure of the logical expression against the natural language translation for accuracy. - Assess the completeness and correctness of interpreting logical operators and quantifiers in translations.
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