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
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
Solution
Solution (Detail)
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.