The student should be familiar with the logical expression if and only if.

If p and q are sentences, then in the conditional sentence "If p, then q,"
p is called the hypothesis, and q, the conclusion. The sentence "If q, then p" is called its converse.

The sentence "p if and only if q" means:

If p then q  and  if q then p.

In other words, it means that a sentence and its converse are both true.

Therefore, when we prove an if and only if statement, we must prove both a proposition and its converse.

Often, if and only if is used to state a definition.  For example,

"r is a root of a polynomial P(x)

if and only if Pr) = 0."