Mathematical Language
Converse of an "If ... then ..". Statement
If we switch the hypotheses and the conclusion of an "If then " statement we get the converse "If then ".
The converse of an "If ... then ... " statement is a new statement with the hypothesis and conclusion
switched: the converse of "If then " is "If then ". For example, the converse of "If (a building is a church) then (the building
is green)" is "If (a building is green) then (the building is a church)". The converse of an "If ... then ... " statement is not equivalent to the original "If ... then ... " statement.
The statement "If , then " is true, but the converse statement "If , then " is not true because makes the hypothesis of the converse true and the conclusion false.