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If A = \( \Large \{ x : x^{2} = 1 \} \) and B \( \Large \{ x : x^{4} = 1 \} \), then \( \Large A \cup B \) is equal to:
A) {i, -i}
B) {-1, 1}
C) {-1, 1, i. -i}
D) None of these
Correct answer:
A) {i, -i}
Description for Correct answer:
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, \( \Large \left(A-B\right) \cup \left(B-A\right) = \{ -i,\ i \} \)
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