Question

If A = {x ∈ C : x² = 1} and B = {x ∈ C : x⁴ = 1}, then write A − B and B − A. 

Answer 1

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}