Correct Answer: {i, -i}

Given that \( \Large A = \{ x:x^{2}=1 \},\ B=\{ x:x^{4}=1 \} \)

=> \( \Large A = \{ -1,\ 1 \},\ B = \{ -1,\ 1,\ -i,\ i \} \)

Now, \( \Large A - B = \phi,\ B-A = \{ -i,\ i \} \)

Therefore, \( \Large \left(A-B\right) \cup \left(B-A\right) = \{ -i,\ i \} \)