logic- translating quantification in english

Question

Let Q(X) be the statement "x has developed a program in JAVA" and P(x) be a statement "x spends more than four hours surfing the internet" where the domain for x consists of the students in ICS.

Q1.) $∀x~P(x)$

A1.) For every x, x spends more than four hours surfing the internet.

Q2.) $∃x~¬Q(x)$

A2.) There is an x such that x has developed a program in JAVA is false.

Q3.) $∀x~(P(X)\to Q(X))$

A3.) For every x, x spends more than four hours surfing the internet then x has developed a program in JAVA.

Are my answers to this correct?

Answer 1

It is not a bad start, but you need to translate completely, rather than mix math symbols and words.   You should talk about students in ICS rather than $x$.

Also you should try for more natural speech , without losing the intent of the sentence.

$\forall x~T(x)$ "Every student in ICS drinks tea."

$\exists x~\neg B(x)$ "Some student in ICS does not eat biscuits."

$\forall x~(T(x)\to B(x))$ "Every student in ICS, who drinks tea, does eat biscuits."

And such.

Answer 2

1. It sounds nicer if you eliminate the variable: "All ICS students spend more than 4 hrs surfing"
2. Idem + ambiguous subclause + get rid of the technical word false: "There is an ICS student who hasn't developed a Java program
3. Eliminate variable + missing if: "All ICS students who spend more than 4 hrs surfing have developed a Java program"

Answer 3

While your answers are correct, you are probably supposed to use a "more natural" language. For example:

1. Every student in ICS spends more than 4 hours surfing the internet.
2. Some student in ICS hasn't developed a JAVA program.
3. Every student in ICS that spends more than 4 hours surfing the internet has developed a JAVA program.