Given the below vocabulary, define the following arithmetic assertions in first$-$order

logic$(FOL).(30pts)$

Even$($s$)$: Unary predicate which tells that $s$ is an even number.

Prime$($s$)$: Unary predicate which tells that $s$ is a prima number.

$x+y$ : Binary function that returns the sum of its two parameters $x$ and $y.$

$x**y$ : Binary function that returns the product of its two parameters $x$ and $y.$

Constant symbols: $0,1,2,$dots.

a$.$ Represent the property $"n$ is an even number" by completing the missing part

in the following sentence.

AAnEven$(n)>$dots

b$.$ Represent the property $"n$ is a prime number" by completing the missing part

in the following sentence.

AAn Prime$(n$

c$.$ Goldbach's conjecture is the conjecture $($unproven as yet$)$ that every even

number is equal to the sum of two primes. Represent this conjecture by

completing the missing part in the following sentence.

AAnEven$(n)=>$dots