{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW2 - 4(1 point A “twin prime pair” is an ordered pair...

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ﬁrst element of the ordered pair. Describe symbolically the set of “twin prime pairs”. 5. (1 point) Use a universal quantiﬁer, and an existential quantiﬁer, to express symbolically the fact that there are inﬁnitely many primes. (Express the fact that whenever you are given a prime, you can ﬁnd 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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

HW2 - 4(1 point A “twin prime pair” is an ordered pair...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online