Final answer:
A conditional statement is made up of an antecedent (the condition) and a consequent (the result). The necessary condition in this statement is that three must be a prime number, while the sufficient condition is that if three is a prime number, then it is only evenly divisible by itself and one.
Step-by-step explanation:
A conditional statement consists of an antecedent (the condition that follows 'if') and a consequent (the result that follows 'then'). In the given conditional statement, the antecedent is 'three is a prime number' and the consequent is 'three is only evenly divisible by itself and one.'
The necessary condition in this statement is that three must be a prime number. This means that three cannot be evenly divisible by any other number except itself and one. The sufficient condition is that if three is a prime number, then it is only evenly divisible by itself and one.
The necessary and sufficient conditions in this statement form a logical relationship where the necessary condition (being a prime number) guarantees the sufficient condition (being evenly divisible only by itself and one).
Hence, the necessary condition in the statement relates to divisibility ('only evenly divisible by itself and one'), whereas the sufficient condition is being a prime number ('three is a prime number').