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 $an Alaskan mountain is$ $more than 20300 ft high,$ then $it is the$ $highest in Alaska .$
Statement III: $Alaska ’ s Mount$ $McKinley is 20320 ft high .$

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 \to q and q \to r then p \to r is true is true, is true .

Applying the Law of Syllogism, we can make a valid conclusion.

\underline{Conclusion I} If an Alaskan mountain is more than 20300 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 \to r and p then r is true is true, is true .

Having used the Law of Detachment, we have the final conclusion shown below.

\underline{Conclusion II} Alaska ’ s Mount McKinley is the highest in the U . S .

Exercise