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Question
If A = {x ∈ C : x2 = 1} and B = {x ∈ C : x4 = 1}, then write A − B and B − A.
Solution
We have:
A = {x ∈ C : x2 = 1}
\[\Rightarrow\] A = {\[-\]1, 1}
And,
B = {x ∈ C : x4 = 1}
\[\Rightarrow\]= {\[x^4 - 1 = 0\]
\[\Rightarrow\]B = {\[\left( x^2 - 1 \right)\left( x^2 + 1 \right)\]
\[\Rightarrow\]B = {\[-\]1, 1,\[-\]i, i}
Thus, we get:
A − B =\[\varnothing\]
And,
B − A = {\[-\]i, i}
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