Question

Determine whether the argument used to check the validity of the following statement is correct: 

p: “If x² is irrational, then x is rational.” 

The statement is true because the number x² = π² is irrational, therefore x = π is irrational.

Answer 1

Argument Used: 

x² = π² is irrational, therefore x = π is irrational. 

p: “If x² is irrational, then x is rational.” 

Let us take an irrational number given by x = √k, where k is a rational number. 

Squaring both sides, we get, 

x² = k 

Therefore, x² is a rational number and contradicts our statement. 

Hence, the given argument is wrong.