143k views
2 votes
Use the Law of Detachment to give a valid conclusion. If not possible, write no valid conclusion.

Use the Law of Detachment to give a valid conclusion. If not possible, write no valid-example-1
User Justinkoh
by
7.2k points

1 Answer

3 votes

Hello there. To solve this question using the Law of Detachment, first we need to remember what does this law refers to:

Say we have two propositions p and q.

If p implies q and p is true, q is also true.

For the transitivity property, we'll have:

If p = q and q = r, then p = r.

We want to show that the angles 30º and 60º are complementary using that law.

Remember that two angles are complementary when their sum is equal to a right angle, i. e. 90º.

Most likely, to get to this conclusion, we may need to show that the sum of those terms in different orders, I mean, 30º + 60º = 90º = 60º + 30º won't change the value.

Thus, we'll get two properties in which we'll get to the same conclusion as the first thing marked down in bold.

Let's assume p is equal to the sum of angle 1 and angle 2.

r is the sum of angle 2 and angle 1 (just changed the order)

You can see that p = q, since 30º + 60º = 90º

and q, being the right angle, will also be equal to r, since 90º = 60º + 30º

Thus, p = r, which leads us to the conclusion.

p implies q, p is true and q is also true.

The angles are complementary.

User Galina Melnik
by
7.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories