Answer: The statement that is not true is
(D) If x² = 1, then x = 1.
Step-by-step explanation: We are given to select the statement that is NOT true.
Statement 1 : If x = 1, then x² = 1.
Let x = 1, then we have
[tex]x^2=1^2=1.[/tex]
So, the statement is TRUE.
Statement 2 : If x = -1, then x² = 1.
Let x = -1, then we have
[tex]x^2=(-1)^2=1.[/tex]
So, the statement is TRUE.
Statement 3 : x² = 1 if and only if x = 1 or x = –1.
Let x = 1 or -1, then we have
[tex]x^2=1^2=1,\\\\x^2=(-1)^2=1.[/tex]
Again, let x² = 1, then
[tex]x^2=1\\\\\Rightarrow x=\pm\sqrt{1}~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=1,~-1.[/tex]
So, x² = 1 if and only if x = 1 or x = –1.
That is, the statement is TRUE.
Statement 4 : If x² = 1, then x= 1.
Let x² = -1, then we have
[tex]x^2=1\\\\\Rightarrow x=\pm\sqrt{1}~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=1,~-1.[/tex]
So, if x² = 1, then x = 1 or x = –1.
Therefore, the statement is NOT TRUE.
Thus, the statement that is not true is (D).
