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If a = {X ∈ C : X2 = 1} and B = {X ∈ C : X4 = 1}, Then Write a − B and B − A. - Mathematics

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

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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}

Concept: Subsets
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.9 | Q 5 | Page 49
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