MHB Truth Table for P(x) & R(x), ~Q(x) & P(x) in U

[trevor]

Consider the following open propositions over the universe U = {− 4,−2, 0, 1, 3, 5, 6,
8, 10}
P(x): x ≥ 4
Q(x): x 2 = 25
R(x): s is a multiple of 2
Find on a single truth table the truth-values of the following.
i. P(x ) ∧ R (x )
ii. [~ Q(x )] ∧ P(x )]

 

[Evgeny.Makarov]

Please note that according to https://mathhelpboards.com/rules/ 11 you are expected to explain your attempts at solving the problem or describe your difficulty. At the very least please make sure that the problem statement is typed correctly and not simply copied, which results in formulas like "x 2 = 25", which don't make sense. And what is $s$ in "$s$ is a multiple of 2" since it is supposed to be the definition of $R(x)$?

Truth tables are not usually used in predicate logic, but since the universe is finite, their use makes sense here. I assume the table should look like this (I use 0 for false and 1 for true).
\[
\begin{array}{r|c|c|c|c|c}
x & P(x) & Q(x) & R(x) & P(x)\land R(x) & \neg Q(x)\land P(x)\\
\hline
-4&0&&1&0&\\
-2&0&&1&0&\\
0&0&&1&0&\\
1&0&&0&0&\\
3&0&&0&0&\\
5&1&&&&\\
6&&&&&\\
8&&&&&\\
10&&&&&
\end{array}
\]
Try filling the rest of the table.