4. (a) Let Q = : a, b e Z, b#0, gcd(a, b) = 1} be the set of rational numbers. An integer p is called a prime number if p has only two factors; 1 and p itself. Prove that p is not a rational number. Hence or otherwise verify the irrationality of V3.

4. (a) Let Q = : a, b e Z, b#0, gcd(a, b) = 1} be the set of rational numbers. An integer p is called a prime number if p has only two factors; 1 and p itself. Prove that p is not a rational number. Hence or otherwise verify the irrationality of V3.

Name: 4. (a) Let Q = : a, b e Z, b #0, gcd(a, b) =1} be the set of rational
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Description: 4. (a) Let Q = : a, b e Z, b #0, gcd(a, b) =1} be the set of rational numbers.An integer p is called a prime number if p has only two factors; 1 and p itself.Prove that p is not a rational number. Hence or otherwise verify theirrationality of V3.(b)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. (a) Let Q = : a, b e Z, b #0, gcd(a, b) =1} be the set of rational numbers.
An integer p is called a prime number if p has only two factors; 1 and p itself.
Prove that p is not a rational number. Hence or otherwise verify the
irrationality of V3.
(b) Consider the statement: if x <y+ e, VE> 0, then r<y. State the
hypothesis P(x, y) and the conclusion Q(x, y) of the statement and prove by
contraposition that the implication P(r, y) → Q(x, y) is true.

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