HW2 - 4. (1 point) A twin prime pair is an ordered pair of...

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Name: Math 100 Due Wednesday, October 10, 2:00 pm Homework 2 The questions below refer to the following sets: I = { n Z such that 1 n AND n 20 } . P is the set of prime numbers. In other words: P = { p N such that p > 1 AND a N , b N , if ab = p then ( a = 1 OR b = 1) . } . E is the set of even numbers. In other words: E = { e Z such that ( n Z such that e = 2 n ) } . T is the set of multiples of 3. In other words: T = { t Z such that ( n Z such that t = 3 n ) } . 1. (2 points) Explicitly describe the following sets below. For example, one might “explicitly describe” the set E I by: E I = { 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 } . (a) P I . (b) ( E T ) I . (c) ( T E ) I . (d) ( T E ) P . 2. (1 point) Express the following sentence symbolically (using the given sets): Every number which is even and a multiple of three is also a multiple of 6. 3. (1 point) Describe symbolically the set of integers which are squares of primes.
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Unformatted text preview: 4. (1 point) A twin prime pair is an ordered pair of prime numbers, such that the second element of the ordered pair is two more than the rst element of the ordered pair. Describe symbolically the set of twin prime pairs. 5. (1 point) Use a universal quantier, and an existential quantier, to express symbolically the fact that there are innitely many primes. (Express the fact that whenever you are given a prime, you can nd a prime which is bigger). 6. (2 points) Is the following statement true or false? Give a convincing argument (in complete and clear English sentences with symbols as necessary) to support your conclusion. p P, x E, y T, such that p + x = y. Page 2...
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HW2 - 4. (1 point) A twin prime pair is an ordered pair of...

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