Start by making a conclusion between the first and second statement. Then, make a final conclusion between the third statement and your first conclusion.
Alaska's Mount McKinley is the highest mountain in the U.S.
Practice makes perfect
We have been given three statements.
Statement I: If a mountain is the highest in Alaska, then it is the highest in the United States.
Statement II: If an Alaskan mountain is more than 20 300 ft high, then it is the highest in Alaska.
Statement III: Alaska's Mount McKinley is 20 320 ft high.
Since the conclusion of Statement II matches the hypothesis of Statement I, let's use the Law of Syllogism to make our first conclusion.
If p → q &is true
and q → r &is true,
then p → r &is true.
Applying the Law of Syllogism, we can make a valid conclusion.
Conclusion I
If an Alaskan mountain is
more than 20 300 ft high,
then it is the highest in the United States.
Next, when we compare Conclusion I and Statement III, we see that Statement III matches the hypothesis of Conclusion I. Thus, we can use the Law of Detachment to make a final conclusion on Statement III and Conclusion I.
If p → r &is true
and p &is true,
then r &is true.
Having used the Law of Detachment, we have the final conclusion shown below.
Conclusion II
Alaska's Mount McKinley
is the highest in the U.S.
