Converse (logic) facts for kids

A converse is a special way to change an "if-then" statement in mathematics and logic. Imagine you have a statement like "If A is true, then B is true." The converse of this statement simply flips it around: "If B is true, then A is true."

Even though the converse uses the same parts as the original statement, they don't always mean the same thing. Just because an "if-then" statement is true, it doesn't automatically mean its converse is also true.

What is a Converse?

A converse takes an original statement and reverses its parts. Think of it like this:

• Original statement: "If it is raining (A), then the ground is wet (B)."
• This can be written as A → B.

The converse of this statement would be:

• Converse: "If the ground is wet (B), then it is raining (A)."
• This can be written as B → A.

Why the Converse Can Be Different

It's important to know that the original statement and its converse are not always the same. The truth of one does not guarantee the truth of the other.

Let's look at our example:

• Original: "If it is raining, then the ground is wet." This statement is usually true. If rain falls, the ground gets wet.
• Converse: "If the ground is wet, then it is raining." This statement is not always true. The ground could be wet because someone used a hose, or because of dew, not just rain.

So, even if the first statement is true, the converse might be false. This shows they are different.

How We Write a Converse

In logic, we often use letters like P and Q to stand for parts of a statement.

• If the original statement is "If P, then Q," we write it as P → Q.
• The converse is "If Q, then P," which we write as Q → P.
• Sometimes, the converse of P and Q is shown with the symbol ←, like P ← Q. This means "P if Q," which is the same as "If Q, then P."

Related pages

• Contrapositive

Images for kids

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  This image shows how a converse flips the parts of a statement.

See also

In Spanish: Conversión lógica para niños