Consider the following states:

$|{}^{+}$:

a$.$ Show that when the $x$ gate is applied to either qubit of $|{}_{+}$:$,$ the result is $|+$:$,$ up to a

global phase.

b$.$ Show that when the $x$ gate is applied to either qubit of $|+$:$,$ the result is $|+$:$,$ up to a

global phase.

c$.$ Show that when the $x$ gate is applied to either qubit of $|,$ the result is $|,$ up to a

global phase.

d$.$ Show that when the $x$ gate is applied to either qubit of $|,$ the result is $|,$ up to a

global phase.