Answer
a. The statement is True because if there is an unique $x$ satisfying $P(x)$ then obviously there is a $x$ satisfying $P(x)$
b. Unless the domain have less than 2 items in it the truth of the hypothesis implies that there is more than one $x$ such for which $P(x)$ holds. Therefore this proposition needs not be True.
c. This is True because if there is a $x$ for which $P(x)$ is False then $P(x)$ clearly does not hold for all $x$.
Work Step by Step
Same as above.
