Writing converses of conditionals
Conditionals, converses, and Euler diagrams
In this lesson we’ll look at how to write a converse statement from a conditional.
Conditionals and converses
We learned in the last section that a conditional statement is an if/then statement where the first part is the hypothesis and the second part is the conclusion.
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They’re written like this:
“If ???A???, then ???B???.”
A converse statement flips around the if/then from the conditional. So instead of “If ???A???, then ???B???,” the converse says
“If ???B???, then ???A???.”
Notice that the converse of a conditional statement is itself a conditional statement.
What are converses of conditional statements, and how do we write them?
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Writing the converse of the conditional statement
Example
Write the converse of the statement.
“If it snows, then they cancel school.”
A converse statement flips around the if/then from the conditional. So we flip the places of “canceling school” and “snow.”
Conditional: “If it snows, then they cancel school.”
Converse: “If they cancel school, then it snows.”
Notice that the conditional statement makes sense and could possibly be true. But this converse doesn’t really make sense because cancelling school doesn’t necessarily mean it will snow.
Let’s look at another example.
Notice that the converse of a conditional statement is itself a conditional statement.
Example
What is the conditional statement represented in the Euler diagram? What is its converse?
This diagram is of the form:
“If ???A???, then ???B???.”
This means the conditional statement is:
“If it’s a rectangle, then it has two pairs of parallel sides.”
For the converse, we switch the places of what goes with the if and the then.
Conditional: “If it’s a rectangle, then it has two pairs of parallel sides.”
Converse: “If it has two pairs of parallel sides, then it’s a rectangle.”
Notice that the converse is not always true. A shape that has two pairs of parallel sides could be any parallelogram, not necessarily a rectangle.
