Part 1.1 on Necessary and Sufficient Conditions (Lecture 4)

• For each claim, rewrite it (1) in terms of necessary and/or sufficient conditions, and also (2) using the if, then format.

• The following examples show the format of answers.

• Assessment weight: 5% (1% for each)

1. This claim would seem plausible only if Alex also thought that there was no way to reject it.

2. Unless I have some special reason to trust my thermometer over yours, it seems as though I should be agnostic about whose thermometer is correct.

3. It is impossible for Hong Kong to conduct comprehensive testing of its 7.5 million residents by itself within a short period of time without external support.

4. A hexagon must have six sides, six vertices, and six edges.

5. Cannibalism can only be morally justified if there is no such thing as human dignity.

Example 1 You can't have a fire without oxygen. Answer 1. "According to the statement, the presence of fire is the sufficient condition for the presence oxygen." or "According to the statement, the presence oxygen is the necessary condition for the presence of fire." (Students should write only ONE correct answer) 2. "If there is a fire, then there is oxygen." or "If there is no oxygen, then there is no fire." (Students should write only ONE correct answer) Markime scheme Correctly rewriting the claim in terms of necessary and/or sufficient conditions: 0.5% Correctly rewriting the claim using the format "if, then": 0.5% Example 2 Only UOWCHK students can use the facilities on Telford campus. Answer 1. "According to the statement, a person being a UOWCHK student is the necessary condition for being allowed to use the facilities on Telford campus." Or "According to the statement, a person who can use the facilities on Telford campus is the sufficient condition for the person being a UOWCHK student." (Students should write only ONE correct answer) 2. "If a person is allowed to use the facilities on Telford campus, then she is a UOWCHK student." or "If a person is not a UOWCHK student, then the person cannot use the facilities on Telford campus." (Students should write only ONE correct answer) Marking scheme Correctly rewrite the claim in terms of necessary and/or sufficient conditions: 0.5% Correctly rewrite the statement using the format "if, then": 0.5%