The notation
∃!xP(x)
denotes the statement
"There exists a unique x such that P(x) is true".
What are the truth values of the following?
a. ∃!x ∈ Z, (x + 3 = 2x)
b. ∃!x ∈ Z, (x = x + 1)
c. ∃!x ∈ Z, (x² = 1)
d. ∃!x ∈ Z, (x > 1)