A converse statement is a conditional statement that switches around the hypothesis and the conclusion. A conditional statement claims that if "a," then "b," and the converse of that states that if "b," then "a."
An example of a conditional statement is, "If it is raining, then the children go inside." The converse of that statement is, "If the children go inside, then it is raining." It is possible to have a conditional statement that is true, but a converse that is false; this is the case in the previous example, because if the children go inside, it does not necessarily mean it is raining.