MA005: Calculus I

If we switch the hypotheses and the conclusion of an "If $A$ then $B$" statement we get the converse "If $B$ then $A$".

The converse of an "If ... then ... " statement is a new statement with the hypothesis and conclusion switched: the converse of "If $(A)$ then $(B)$" is "If $(B)$ then $(A)$". 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 $x = 2$, then $x^2 = 4$" is true, but the converse statement "If $x^2 = 4$, then $x = 2$" is not true because $x = –2$ makes the hypothesis of the converse true and the conclusion false.