need help with 2 quick very basic and short few questions assignment for a philosophy class - topics are logic/reasoning. 2 problem sets with questions and 2 modules for the set are included as attach

PHIL 1300: Introduction to Logic

Problem Set 1

1 Logical Consequence

1. Are the following arguments valid or invalid? If the argument is invalid, briefly explain why.

If the argument is sound, explain how you know.

1. Ottawa is east of Winnipeg.
2. Montreal is east of Ottawa.
3. ∴ Montreal is east of Winnipeg.

1. Vancouver is the capitol of Canada.
2. Canada is located in the southern hemisphere.
3. ∴ Vancouver is located in the southern hemisphere.

1. Some students who take introductory logic find the course challenging.
2. Ange is a student in introductory logic.
3. Ange has a 4.0 average across all her courses.
4. ∴ Ange does not find introductory logic challenging.

1. Some students who take introductory logic find the course challenging.
2. Ange is a student in introductory logic.
3. Ange has a 4.0 average across all her courses.
4. ∴ Either Ange finds introductory logic challenging, or she doesn’t.

2. Is it possible to make a valid argument invalid by adding a premise? Why or why not?

2 Logical Properties

1. What is necessary equivalence? Give an example of three logically equivalent sentences.

2. What is it for a set of sentences to be jointly impossible? Give an example of three jointly impossible sentences.

3 Necessary and Sufficient Conditions

1. Provide an example of a necessary condition for each of the following events:

(a) The Winnipeg Jets make it to the Stanley Cup finals in 2021.

(b) Justin Trudeau is Prime Minister of Canada in 2022.

2. Provide an example of a sufficient condition for each of the following events:

(a) A member of the Liberal Party is Prime Minister of Canada in 2020.

(b) A female is President of the United States in 2026.