Questions: P: Some mountain ranges have cold weather. P: Ottawa (x) has cold weather. C: Ottawa is a mountain range. a. Is the argument valid? NO b. Create a Venn diagram of the premises that supports the correct answer. c. Is the argument sound? NO

P: Some mountain ranges have cold weather.
P: Ottawa (x) has cold weather.
C: Ottawa is a mountain range.
a. Is the argument valid? NO
b. Create a Venn diagram of the premises that supports the correct answer.

c. Is the argument sound? NO

Transcript text: P: Some mountain ranges have cold weather. P: Ottawa $(x)$ has cold weather. C: Ottawa is a mountain range. a. Is the argument valid? $\square$ NO O b. Create a Venn diagram of the premises that supports the correct answer. c. Is the argument sound? $\square$ NO

Solution

Solution Steps

Step 1: Analyze the argument

The argument states: P1: Some mountain ranges have cold weather. P2: Ottawa (x) has cold weather. C: Ottawa is a mountain range.

This argument attempts to conclude that Ottawa is a mountain range because it has cold weather, and some mountain ranges also have cold weather.

Step 2: Determine the validity of the argument

The argument is invalid. Just because Ottawa has cold weather and some mountain ranges have cold weather doesn't guarantee that Ottawa is a mountain range. Many other places that aren't mountain ranges have cold weather. The Venn diagram in the problem demonstrates this. The 'x' representing Ottawa is placed within the "Places with cold weather" circle, but outside the "Mountain Ranges" circle. It shows that Ottawa can have cold weather without being a mountain range.

Step 3: Determine the soundness of the argument

Since the argument is invalid, it cannot be sound. A sound argument must be both valid and have true premises.