Determine whether the argument used to check the validity of the following statement is correct: p: “If x 2 is irrational, then x is rational.” The statement is true because the number x 2 = π 2 is irrational, therefore x = π is irrational.

Question

Philoid · Accepted Answer

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.

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.

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.