In geometry, converse, inverse and contrapositive are conditional statements consisting of a hypothesis and a conclusion. These statements are also known as “if-then statements.” The hypothesis part of a conditional statement is the “if," and the “then” part is the conclusion. The conclusion is the result of a hypothesis.
A conditional statement is represented in geometry by the symbols "if p, then q." The p represents the hypothesis and the q represents the conclusion.
Example: “If it is sunny, then I will wash my car.”
The converse of a conditional statement occurs when the hypothesis and the conclusion switch places. Instead of "if p, then q," the converse is "if q, then p."
Example: “If I wash my car, then it is sunny.”
The inverse of a conditional statement is when both the hypothesis and the conclusion are negated. The symbols of a negated hypothesis and conclusion are ~p and ~q meaning "if not p, then not q."
Example: “If it is not sunny, then I will not wash my car.”
The contrapositive of a conditional statement is when both the hypothesis and conclusion have switched places and have been negated. In other words, it is a negated converse statement, "if not q, then not p."
Example: “If I do not wash my car, then it is not sunny.”