A conditional math sentence is one that includes an if, then statement. The implied sentence is if A, then B; where A is a premise and B is the consequence. For example, "if it is raining, then I carry my umbrella." The implied condition has an inverse, contradiction, converse and contrapositive, each of which is true or false.
A converse math sentence is the reverse of an original implied sentence. For the implication "if A, then B," the converse is "if B, then A." The converse is not necessarily true meaning the conclusion of the converse does not have to accepted. The truth of the converse statement is logically unrelated to the truth of the implied statement.
For the previous example, "if it is raining, then I carry my umbrella" the converse sentence is "If I carry my umbrella, then it is raining." For the statement, "If it is a dog, then it is a mammal" with converse "if it is a mammal, then it is a dog," the converse is false as an absolute statement, while the original implication is always true. Alternately, "if a shape has four sides, then it is a quadrilateral" is always true in both the implied and converse forms.
Conditional sentences include the inverse, contradiction or contrapositive of an original implied condition. For the "if A, then B" statement, the inverse is "if not A, then not B." The contradiction is "if A, then not B." The contrapositve is "if not B, then not A."