Identify the correct translation into logical notation of the following…
2007
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: taller (x, y) is true if x is taller than y.
- A.
(∃x)(boy(x) → (∀y)(girl(y) ∧ taller(x, y)))
- B.
(∃x)(boy(x) ∧ (∀y)(girl(y) ∧ taller(x, y)))
- C.
(∃x)(boy(x) → (∀y)(girl(y) → taller(x, y)))
- D.
(∃x)(boy(x) ∧ (∀y)(girl(y) → taller(x, y)))
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Correct answer: D
To translate 'Some boys... are taller than all the girls': 1. 'Some boys' requires an existential quantifier ($\exists x$) with a conjunction ($\land$). 2. 'All the girls' requires a universal quantifier ($\forall y$) with an implication ($\to$). 3. The relationship is $taller(x, y)$. Combining these yields $(\exists x)(boy(x) \land (\forall y)(girl(y) \to taller(x, y)))$. This corresponds to Option 3.
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