Determine whether you can use the Law of Syllogism to reach a valid conclusion from each set of statements.

Question

1. If a dog eats Superdog Dog Food, he will be happy.
Rover is happy.

2. If an angle is supplementary to an obtuse angle, then it is acute.
If an angle is acute, then its measurement is less than 90.

3. If the measure of angle A is less than 90, then angle A is acute.
If angle A is acute, then angle A is congruent to angle B.

Answer 1

Let's take the first one.

You can make a syllogism if you have two statements like:

(1) If A, then B _and_
(2) Rover is A
(3)_then_ you can say that Rover is B

Now:
(1) If a dog eats Superdog Dog Food, he will be happy.
(2) Rover is happy.

What is "A" here? it's "eats Superdog Dog Food". Does (2) say anything about "eats Superdog Dog Food"? No. So you don't have a syllogism. Rover might or might not eat Superdog Dog Food; we don't know.

So there is no syllogism here.

Now try the other two.

Answer 2

If an angle is a right angle, then the measure of the angle is 90. If two lines are perpendicular, then they form a right angle.