Show that there are irrational numbers x,y ε R such that 2x - y is rational

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Since you are trying to prove existence, you only have to show an example to prove the claim.π is irrational.x = π/2 and y = π.2x - y = 2(π/2) - π = π - π = 0.0 is a rational number.You can prove there are infinitely many x, y pairs by:Let z be an irrational number. Let x = z/2 and y = z.2x - y = 2(z/2) - z = z - z = 0. Since there are infinitely many values of z, there are infinitely many pairs of x and y such that 2x - y is a rational number.