Proficiency #1. [Statements] Which of the following sentences are statements? Do not worry about whether they are true or false. (Choose all that are correct.) I. 82 + 152 mod 17. II. Every irrational number m can be written as , where x and y are irrational numbers. III. For every odd integer k, k³ + 37k2 – 42k +1 is prime. IV. {r € Z|r² < 50} V. If n is an even natural number and n 2 4, then there exist primes p and q such that n = p+q. VI. {ACZ|5 € A} = 0.

Proficiency #1. [Statements] Which of the following sentences are statements? Do not worry about whether they are true or false. (Choose all that are correct.) I. 82 + 152 mod 17. II. Every irrational number m can be written as , where x and y are irrational numbers. III. For every odd integer k, k³ + 37k2 – 42k +1 is prime. IV. {r € Z|r² < 50} V. If n is an even natural number and n 2 4, then there exist primes p and q such that n = p+q. VI. {ACZ|5 € A} = 0.

Name: Proficiency RedosProficiency #1. [Statements] Which of the following
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Description: Proficiency RedosProficiency #1. [Statements] Which of the following sentences are statements? Do notworry about whether they are true or false. (Choose all that are correct.)I. 82 + 152 mod 17.II. Every irrational number m can be written as , where

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Proficiency Redos
Proficiency #1. [Statements] Which of the following sentences are statements? Do not
worry about whether they are true or false. (Choose all that are correct.)
I. 82 + 152 mod 17.
II. Every irrational number m can be written as , where x and y are irrational numbers.
III. For every odd integer k, k³ + 37k2 – 42k +1 is prime.
IV. {x € Z | x² < 50}
V. If n is an even natural number and n 2 4, then there exist primes p and q such that
n = p+q.
VI. {ACZ|5 E A} = 0.

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Definition 0.1. Let a and b be two integers. We say that a divides b if there is an integer q so that b = aq. We will use the notation alb as shorthand for this property. Proposition 0.2. Let a, b, and c be integers. If a|b and ale then a|(b+ c). Proposition 0.3. Let a, b, and c be integers. If alb then albc. Question 0.4. Which integers divide zero? Which are divisible by zero? Proposition 0.5. Let a, b, and c be integers. If alb and alc then a|(b – c). Question 0.6. Which integers divide one? Which are divisible by one? Proposition 0.7. Let a, b, c, s and t be integers. If alb and alc then a|(sb+ tc). Proposition 0.8. Let a, b, and c be integers. If a|b and b|c then alc. Question 0.9. Does 2|4? Does 2|3? How can you prove your answers?
Discrete Math