Determine whether the argument used to check the validity of the follo

1.	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» Argument Used: x² = π²is 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.

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»

Argument Used:

x² = π²is 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.