Use the Law of Detachment to write a valid conclusion for the given information.
1.If two angles are supplementary, then their measures have a sum of 180.
2.Angle X and Angle Y are supplementary.
-What do they mean when they ask me to write a valid conclusion?
The law of detachment, better known as Modus Ponens, can be expressed as p=>q, or if p is true, then q must be true.
For example,
p=it does not rain
q=I will go outside
so
If I say
If it does not rain, then I will go outside.
And if today it does not rain, a valid conclusion will be I will go outside.
If it does not rain today, I do not have a valid conclusion.
See if you can draw a valid conclusion from the given statements 1 and 2.
When they ask you to write a valid conclusion, they are asking you to draw a logical inference based on the given information using the Law of Detachment. In other words, you need to make a statement that follows directly from the given premises.
When they ask you to write a valid conclusion using the Law of Detachment, it means that you need to make a logical statement based on the given information that follows the format of the Law of Detachment. The Law of Detachment states that if a conditional statement "if p, then q" is true and its hypothesis (p) is true, then its conclusion (q) must also be true.
In this scenario, the conditional statement is "If two angles are supplementary, then their measures have a sum of 180" (1). The second statement "Angle X and Angle Y are supplementary" (2) confirms that the hypothesis of the conditional statement is true because it states that Angle X and Angle Y are supplementary.
To apply the Law of Detachment, we use the given information to conclude that Angle X and Angle Y have measures that sum to 180.
Therefore, a valid conclusion using the Law of Detachment is: "Angle X and Angle Y have measures that sum to 180 degrees."