MAT22A-Waldron-Fall-2010.awlee.Homework0-Background

MAT22A-Waldron-Fall-2010.awlee.Homework0-Background -...

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Alexander Lee MAT22A-Waldron-Fall-2010 WeBWorK Homework0-Background is due : 09/29/2010 at 03:00pm PDT. Visit http://www.math.ucdavis.edu/ wally/teaching/22A/22A.html for the syllabus, grading policy and other information. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TAs or your professor for help. Don’t spend a lot of time guessing – it’s not very efficient or effective. Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin ( 3 * pi / 2 ) instead of -1, e ( ln ( 2 )) instead of 2, ( 2 + tan ( 3 )) * ( 4 - sin ( 5 )) 6 - 7 / 8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professor. Logical quantifiers The sentence A B is read ”A implies B” and means that whenever A is true, B is also true. That is, A B means ”if A, then B.” For example, I am in Davis I am in California, because if I am in Davis, then I am in California. Or, x is a multiple of four x is even, because if a number is a multiple of four, then it must surely be even. Similarly, the sentence A B is read ”A is implied by B” and means that whenever B is true, A is also true. That is, A B means ”if B, then A,” or, equivalently, ”B only if A.” For example, sin x = 0 x = 0 or - π , because if x = 0 or π then sin x = 0 . The sentence A B means exactly the same thing as the sen- tence B A . Notice that in all of the above examples, we cannot reverse the arrow. That is, the following statements are FALSE: I am in California I am in Davis. x is even x is a multiple of four. sin x = 0 x = 0 or - π . The first is false because if I am in California, I might be in Los Angeles; the mere fact that I am in California is not enough to tell me without a doubt that I am in Davis. The second is false because if a number is even, it does not have to be a multiple of four–for example, six is even but not a mul- tiple of four. The third is false because if sin x = 0 , x could be ANY integer multiple of π , not just 0 or π . In some situations, we CAN reverse the arrow. That is, some- times A B AND B A . In this case, we write A ⇐⇒ B , read ”A if and only if B.” Sometimes this is abbreviated ”A iff B” in writing. For example,
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MAT22A-Waldron-Fall-2010.awlee.Homework0-Background -...

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