Law of Detachment

How to use the law of detachment to find the statement that is always true: the law, 1 example, and its solution.

Law

Law

If a conditional [p → q] and its hypothesis [p]
are both true,
then its conclusion [q] is true.

This is the law of detachment.

Conditional Statement: Truth Value

Example

Example

Solution

The first statement is a conditional statement.

So the statement behind if is p:
it's raining.

And the statement behind then is q:
I'm staying home.

So the first statement is p → q.

Then the second statement is p.

It says
both [p → q] and [p] are true.

Then, by the law of detachment,
the conclusion [q] is true.

Write q:
I'm staying home.

So

I'm staying home

is always true.