Correlations in Spin-Singlet states

[BREAD]

Homework Statement

Homework Equations

The Attempt at a Solution

In (b), if particle B has up spin (x-axis), then A should have down-spin(x-axis). The problem ask the state by using lma,mb> state.
This state is valid only in z-axis, but how can i represent that state ??
I think the answer is the same with (a) regardless of the x-axis measurement

 

[vela]

You could try changing to the basis of eigenkets of $J_x$ and then changing back.