Let $ P = \left\{1,2,3,4\right\}$ and $ R = \left\{x \in \mathbb{Z} | -4 \leq x \leq 4 \right\}$. In each case, check if the given law defines a $ P $ function with values in $ R $, justifying:
a) $y \leq x$ b) $y= -x$ c) $y= \sqrt{x}$
Attemp: If I'm understanding this problem correctly, then for a) it will be that all 4 values in P work, as 4 is greater than or equal to all of 1,2,3,4, and for b) it will again be that all four work, because for 1 it's -1, for 2 it's -2, for 3 it's -3, and finally for 4 it's -4. For c), only 1 and 2 work because for 3 and 4 their squares are greater than 4
Am I right?