Law of Syllogism
How to use the law of syllogism to find the statement that is always true: the law, 1 example, and its solution.
If [p → q] and [q → r] are both true,
then [p → r] is true.
This is the law of syllogism.
The first statement is a conditional statement.
So the statement behind if is p:
And the statement behind then is q:
I'm staying home.
So the first statement is p → q.
The second statement is also
a conditional statement.
The statement behind if is q.
And the statement behind then is r:
I'm listening to music.
So the second statement is q → r.
both [p → q] and [q → r] are true.
Then, by the law of syllogism,
[p → r] is true.
Write p → r.
If, p, it's raining,
then, r, I'm listening to music.
If it's raining,
then I'm listening to music
is always true.