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GATE | GATE-CS-2004 | Question 23

  • Difficulty Level : Medium
  • Last Updated : 28 Jun, 2021

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.

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(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)

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.

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