Let 𝑥 and 𝑦 be real numbers. If 𝑥𝑦 is irrational, then 𝑥 is irrational or 𝑦 is irrational

Kaylynn Cook

Kaylynn Cook

Answered question

2022-11-10

Let x and y be real numbers. If xy is irrational, then x is irrational or y is irrational

Answer & Explanation

Samuel Hooper

Samuel Hooper

Beginner2022-11-11Added 15 answers

The contrapositive of ( x y is irrational x is irrational or y is irrational) is:
x is rational and y is rational x y is rational.
Pf: Let x = a b ; a , b Z And y = c d ; c , d Z
The x y = a b c d = a c b d . And a c Z and b d Z so a c b d is rational.

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