Is $∃!x(x^2 = 1)$ true? for a question that I have it is asking for the truth value of $∃!x(x^2 = 1)$ my instincts tell me no because there are 2 values that make it true. Am I right?

It depends on $x$. If $x > 0$, or $x < 0$ then it's true. But if $x$ is any real number or complex number, then it's false since there are $2$ answers: $x = \pm 1$. And let's say if $x < -3$, then there is no solution.
