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The table below shows the values of predicate $P(x,y)$ for every possible combination of values of the variables $x$ and $y.$ The row number indicates the value for $x$ and the column number indicates the value for $y.$ The domain for $x$ and $y$ is $\{1,2,3,4\}.$

Ex: $P(3,1)$ is true because the entry in row $3,$ column $1$ is $T.$

$x+$

$\backslash$table$[[$P$,1,2,3,4],[1,$F$,$T$,$T$,$T$],[2,$T$,$F$,$T$,$T$],[3,$T$,$T$,$F$,$T$],[4,$T$,$F$,$F$,$T$]]$

Determine the truth value of each expression.

$(1)$