Arithmetic assertions can be written in first-order logic with the predicate symbol <, the function symbols + and ×, and the constant symbols 0 and 1. Additional predicates can also be defined with biconditionals.

a. Represent the property “x is an even number.”

b. Represent the property “x is prime.”

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 as a logical sentence.