Consider the sentence below.

There is a country that borders both India and Pakistan.

Which of the following logical expressions express the above sentence correctly when the predicate $Country(x)$ represents that $x$ is a country and $Borders(x,y)$ represents that the countries $x$ and $y$ share the border?

The sentence says there exists some country $c$.

So, we use existential quantifier:

$\exists c$

That country must satisfy three conditions:

$c$ is a country.

$c$ borders India.

$c$ borders Pakistan.

So, the correct expression is:

$\exists c\ [Country(c)\land Border(c,India)\land Border(c,Pakistan)]$

Option (b) is incorrect because implication does not force $c$ to be a country that borders both.

Option (c) is incorrect because it separates existence of country from border condition.

Option (d) is syntactically incorrect because $Country(c)$ is a predicate, not an object to be used inside $Border$.