Prove that if x^3 is irrational, then x is irrational
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Solution Using Proof by Contradiction
Let p: be "x3 is irrational" and q be "x is irrational"
we can assume that p implies ¬q is true, when p is true and ¬q is true
Interpreting this, "x3 is irrational" and "x is not irrational"
Now, if "x is not irrational" is true, then "x is rational" will also be true
Using proof by contradiction to show that x3 is irrational by proving that x is rational
let x = a∕b, where a is a set of all real numbers and b ≠ 0
Since, we've shown that x is rational
∴ x3 = a3∕b3
x * x * x * b * b * b = a * a * a