Converses
| If in a statement, the hypothesis and the conclusion are interchanged with maybe a slight change in its structure, the new statement is called the converse of the original statement. |
Let's return to our familiar example, "If it is raining, then I’ll bring an umbrella."
The converse would be "If I bring an umbrella, then it is raining."
Another example:
In "If two triangles are congruent, then their corresponding angles are congruent", the component "two triangles are congruent" is the hypothesis and the component "their corresponding angles are congruent" is the conclusion.
The converse of the statement would be "If the corresponding angles of two triangles are congruent, then the triangles are congruent."
If we define p: two triangles are congruent and q: their corresponding angles are congruent, then
.
The converse would be
.
