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)))
Answer: (D)
Explanation:
Now many people get confused when to use ∧ and when to use →. This question tests exactly that.
We use ∧ when we want to say that the both predicates in this statement are always true, no matter what the value of x is.
We use → when we want to say that although there is no need for left predicate to be true always, but whenever it becomes true, right predicate must also be true.
D means there exist some boys x which taller than all girls y.