9. In this question I am assuming you know what a prime number is; if not, take a look at the definition on page 69. For each of the following statements, form its negation and either prove that the statement is true or prove that its negation is true: (a) ▼n E Z such that n is a prime number, n is odd. (b) Vn E Z, 3a, b,c,d,e,f,g,hE Z such that = a² +b³ +c³ +d³ +e° + f³ + g³ +h°. n =

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9. In this question I am assuming you know what a prime number is; if not,
take a look at the definition on page 69.
For each of the following statements, form its negation and either prove
that the statement is true or prove that its negation is true:
(a) Vn E Z such that n is a prime number, n is odd.
(b) Vn E Z, 3a, b,c,d,e,f,g,hE Z such that
n = a° +b³ +c³ + d³ + e³ + ƒ³ + g³ +h³.
(c) Ex E Z such that Vn E Z, x # n²+2.
(d) Ex E Z such that Vn E Z, x ±n+2.
(e) Vy e {x\x € Z, x > 1}, 5y² + 5y+1 is a prime number.
(f) Vy € {x\x € Z, x² < 0}, 5y² + 5y+ 1 is a prime number.
Transcribed Image Text:9. In this question I am assuming you know what a prime number is; if not, take a look at the definition on page 69. For each of the following statements, form its negation and either prove that the statement is true or prove that its negation is true: (a) Vn E Z such that n is a prime number, n is odd. (b) Vn E Z, 3a, b,c,d,e,f,g,hE Z such that n = a° +b³ +c³ + d³ + e³ + ƒ³ + g³ +h³. (c) Ex E Z such that Vn E Z, x # n²+2. (d) Ex E Z such that Vn E Z, x ±n+2. (e) Vy e {x\x € Z, x > 1}, 5y² + 5y+1 is a prime number. (f) Vy € {x\x € Z, x² < 0}, 5y² + 5y+ 1 is a prime number.
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