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 r 0, then r

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4. (a) Let Q = {: a, b e Z, b+ 0, gcd(a, b) = 1 be the set of rational numbers.
%3D
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 r <y+ e, VE > 0, then r<y. State the
hypothesis P(r, y) and the conclusion Q(x, y) of the statement and prove by
contraposition that the implication P(x, y) → Q(x, y) is true.
Transcribed Image Text:4. (a) Let Q = {: a, b e Z, b+ 0, gcd(a, b) = 1 be the set of rational numbers. %3D 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 r <y+ e, VE > 0, then r<y. State the hypothesis P(r, y) and the conclusion Q(x, y) of the statement and prove by contraposition that the implication P(x, y) → Q(x, y) is true.
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