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Identify the correct translation into logical notation of the following assertion.

Some boys in the class are taller than all the girls

Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$.

  1. $(\exists x) (\text{boy}(x) \rightarrow (\forall y) (\text{girl}(y) \land \text{taller}(x, y)))$
  2. $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \land \text{taller}(x, y)))$
  3. $(\exists x) (\text{boy}(x) \rightarrow (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
  4. $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
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7 Answers

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Some boys in the class are taller than all the girls.

Our domain is $\textbf{set of boys & girls in the whole class.}$

We rewrite like this:

$\text{There exists some x such that x is boy}\; \color{Red}\text{and}$ $\text{for all y, if y is girl, then x is taller than y}$

logically we can write: $\color{DarkRed}(\exists x) \text{(boy(x)} \wedge (\forall y)(\text{girl(y) → taller(x,y))})$

$\color{DarkGreen}\text{Ans: D}$
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learn one small trick 

---------------------------------------

Use ∧    for there exist(∃)

 Use →   for all(∀)

according to this a and c are gone

remaining b and d 

We use ∧ when we want to say that the both predicates are always true

We use ⟹ when we want to say that although there is no need for left predicate to be true

according to this opyion d is the only option remaining. 

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Trick:- Use ^ for there exist(∃) and use -> for all(∀).Use ^ for there exist(∃) and use -> for all(∀) and find out the answer which comes as option (D).

Answer:

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