Necessary & Sufficient Conditions Practice

Necessary

-A necessary condition is one that is needed for the other half of the conditional statement to be true. -The assertion that a statement is a "necessary and sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false. -A necessary condition is required for something else to happen, but it does not guarantee that the something else happens.

Living in Alabama is ______________ for living in Tuskegee (CHOOSE EXACTLY TWO ANSWERS) A. Necessary B. Not Necessary C. Sufficient D. Not Sufficient

Necessary & Not Sufficient Living in Alabama is necessary for living in Tuskegee. Tuskegee is a city in the state of Alabama. This is why living in the state of Alabama is a requirement for living in the city of Tuskegee. Another way of putting this is that... if you don't live Alabama then you don't live in Tuskegee. However, living in Alabama is NOT sufficient for living in Tuskegee. Tuskegee is one city in the state of Alabama, but there are many other cities as well. So, living in the state of Alabama does NOT guarantee that you live in the city of Tuskegee because you could live in any of the other cities in Alabama. As an example, I live in Auburn. Auburn is a city in Alabama. So, I live in Alabama. This means I live in Alabama but I don't live in Tuskegee. I (Samuel Taylor) am therefore a counterexample that shows that the claim "living in Alabama is sufficient for living in Tuskegee" is wrong. Another way to check this is to think that the claim "living in Alabama is sufficient for living in Tuskegee" can be translated to the following conditional "IF you live in Alabama, then you live in Tuskegee;" this conditional is clearly false and so we know that living in Alabama is NOT sufficient for living in Tuskegee.

Getting at least 90% (ignore cases of potential rounding from participation) in this class is _________________ for getting an A in this class (CHOOSE EXACTLY TWO ANSWERS). a. Necessary b. Not Necessary c. Sufficient d. Not Sufficient

Necessary & Sufficient Getting at least 90% in this class is necessary for getting an A in this class. The grading scheme indicated on the syllabus says that 90%-100% in the course will be given a final grade of an A. This means that if you do NOT get 90% in the class (with any rounding), then you will NOT get an A. So, getting at least 90% (with any rounding) is a requirement for getting the grade of an A. Getting at least 90% in this class is sufficient for getting an A in the class. Given the grading scheme indicated on the syllabus, IF you get at least 90% in the class THEN that guarantees that you'll get an A in the course. Getting at least 90% is enough to get you an A.

Sufficient

-A sufficient condition is one that is enough to guarantee the truth of the other part of the statement, though there may be other conditions that could also affirm the statement to be true. -The statement A is said to be a sufficient condition for the statement B if knowing that A is true guarantees that B is also true. However knowing that B is true does not guarantee that A is true. That is, B needn't be a sufficient condition for A. -An argument is sufficient if, assuming the premises to be true, they are 'enough' to guarantee the conclusion to be true. If an argument's premises are sufficient then it is a deductive argument. -A sufficient condition guarantees the truth of another condition, but is not necessary for that other condition to happen.

Having the highest IQ among the students in the class is ________________ for getting the highest grade in the class (CHOOSE EXACTLY TWO ANSWERS) A. Necessary B. Not Necessary C. Sufficient D. Not Sufficient

Not Necessary & Not Sufficient EXCELLENT! Having the highest IQ among students in the class is NOT necessary for getting the highest grade in the class. NOTE: There are a lot of problems with IQ tests... due to bias and various other worries, it isn't clear that "IQ" actually measures intelligence. Nonetheless, a student with a lower "IQ" (regardless of what this measures) could still put in more work, complete more assignments, and thereby earn the highest grade for this class. Having the highest IQ is not required to get the highest grade in the class. Your grade is determined by the quality of work you turn in. It isn't determined by any controversial measurement of "IQ". Having the highest IQ among students in the class is NOT sufficient for getting the highest grade in the class. NOTE: There are a lot of problems with IQ tests... due to bias and various other worries, it isn't clear that "IQ" actually measures intelligence. Nonetheless, even if a student has the highest "IQ" (regardless of what this measures) might end up skipping assignments, waiting until the last minute and turning in rushed/incomplete work, etc. and thereby end up getting a lower grade than other students in the course. As mentioned above, your grade is determined by the quality of work you turn in. It isn't determined by any controversial measurement of "IQ". So, having the highest "IQ" does not guarantee that you'll get the highest grade.

Taking ALL the quizzes in this class is _________________ for passing this class (CHOOSE EXACTLY TWO ANSWERS) A. Necessary B. Not Necessary C. Sufficient D. Not Sufficient

Not Necessary & Not Sufficient Excellent! Taking ALL the quizzes is NOT necessary for passing this class. There are a few reasons for this. First, you get to drop your lowest quiz in the course. If you skip one quiz and get a zero. It will drop. As long as you do well on all the other assignments, you could still pass. Moreover, the quizzes are worth 20% of your final grade. So, if you got 100% on every other assignment, you could technically skip all the quizzes and your final grade would be 80% which is a passing grade without taking any of the quizzes. (NOTE: I would NOT recommend trying this. Despite being a mathematical possibility, it is entirely unrealistic that it would ever happen. Another way to make this same point is that the statement "Taking ALL the quizzes is necessary for passing this class" can be translated to the following conditional "If you do NOT take ALL the quizzes, then you will NOT pass this class." This conditional claim is false. So, the claim that taking all the quizzes is necessary to pass is also false. Taking ALL the quizzes is NOT sufficient for passing this class. This is because taking all the quizzes does not guarantee that you will pass the class. Even if you take all the quizzes, you could do terribly and fail all the quizzes that you do take (and fail all the other assignments you complete as well. Similarly, if you took all the quizzes but skipped every other assignment in the course then the highest grade you could possibly get is 20% in the course which is a failing grade. So, merely taking all the quizzes would not guarantee that you'll pass. Another way to make this same point is that the statement "Taking ALL the quizzes is sufficient for passing this class" can be translated to the following conditional "If you take ALL the quizzes, then you will pass this class." This conditional claim is clearly false (as we've seen). So, the claim that taking all the quizzes is sufficient to pass is also false.

Getting at least 95% in this class is ______________ for getting an A in this class (CHOOSE EXACTLY TWO ANSWERS) A. Necessary B. Not Necessary C. Sufficient D. Not Sufficient

Not Necessary & Sufficient EXCELLENT! Getting at least 95% in this class is NOT necessary for getting an A in this class. You are not required to get that high of a grade to be given an A. The grading scheme on the syllabus says that 90%-100% is an A. This means that there are grades lower than 95% that will still earn you an A, and so you don't need to get at least 95% to get an A. Imagine a student Robert who earns a 92% in the class would get an A according to the grading scheme on the syllabus. Robert would get an A in the class without getting at least 95%. Robert would thereby be a counterexample to the claim that getting at least 95% is necessary to get an A. Another way to think through this is as follows. The claim "Getting at least 95% in this class is necessary for getting an A" can be translated into the conditional "If you do NOT get at least 95% in this class then you do NOT get an A in this class." This conditional claim is false since you can get an A with a grade between 90% and 94.9%. Since the conditional claim is false, we also know that the claim that getting at least 95% is necessary to get an A is also false. Getting at least 95% in this class is sufficient for getting an A in this class. As I mentioned, the grading scheme says that any grade in the 90%-100% range will get an A. Any grade that is at least 95% is within this range. So, IF you get at least 95% THEN that thereby guarantees that you'll get an A.

Living in San Fransisco is _________________ for living in California (CHOOSE EXACTLY TWO ANSWERS). A. Necessary B. Not Necessary C. Sufficient D. Not Sufficient

Not Necessary & Sufficient Living in San Fransisco is NOT necessary for living in California. San Fransisco is one city in the state of California and living in San Fran. is thereby one way for someone to live in California. However, there are other cities in the state of California and thus there are other ways someone could live in California. Another way to see this is to remember that the claim "Living in San Fran. is necessary for living in California" can be translated to "If you do NOT live in San Fran then you do NOT live in California." This conditional claim is false. There are lots of people who do NOT live in San Fran but still live in California. Since this conditional claim is false, we know that living in San Fran is NOT necessary for living in California. Another way to see this is to think of a counterexample. Consider a person Jasmine who lives in LA. LA is a city in the state of California. Jasmine does not live in San Fran. but she does live in California. This shows that you do not need to live in San Fran. in order to live in California. Living in San Fran. is sufficient for living in California. As you know, San Fransisco is a city located in the state of California. This means that IF someone lives in the city of San Fransisco THEN this guarantees that they also live in the state of California. Living in San Fran. is enough for living in California.