Question 472950
If Sally is on vacation, then Tom is at work.
If Tom is at work, then the line at the post office is long.
Therefore, if Sally is on vacation, then the line at the post office is long.
I believe this is true by the following law:
Law of syllogism: (Law of hypothetical syllogism) (reasoning by transitivity)
This law states:
p -> q (premise 1)
q -> r (premise 2)
therefore:
p -> r (conclusion)
a reference that includes that law as one of the valid arguments is shown below:
<a href = "http://ux.brookdalecc.edu/fac/tlt/math/136/logic.pdf" target = "_blank">http://ux.brookdalecc.edu/fac/tlt/math/136/logic.pdf</a>
search for:
law of syllogism (Law of hypothetical syllogism) (reasoning by transitivity)
here's another reference.
<a href = "http://alameda.peralta.edu/Projects/20430/Logic...%20Philosophy%20010/Deductive%20argument%20forms.htm" target = "_blank">http://alameda.peralta.edu/Projects/20430/Logic...%20Philosophy%20010/Deductive%20argument%20forms.htm</a>
search for:
hypothetical syllogism.