The domain for variable x is the set $\{$Luke$,$Han,Darth,Yoda$\}.$ The table below gives the values of predicates A and B$.$ for every element in the domain.

Name

A$($x$)$

B$($x$)$

Luke

F

F

Han

T

F

Darth

T

T

Yoda

T

T

Select the statement that is false.

Group of answer choices

$$x$($A$($x$)->$B$($x$))$

$$x$(($x$!=$Darth$)$A$($x$)$B$($x$))$

$$x$(($x$!=$Luke$)->($A$($x$)$B$($x$)))$

$$x$($A$($x$)->$B$($x$))$