- Thread starter
- #1

- Thread starter dwsmith
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- Thread starter
- #1

- Feb 5, 2012

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Hi dwsmith,$(A - B)\cup B = A$ iff $B\subseteq A$.

Suppose $B\subseteq A$.

$$

\begin{array}{lcl}

(A - B)\cup B & = & (A\cap B^c)\cup B\\

& = & (A\cup B)\cap (B^c\cup B)\\

& = & A\cap B\\

& = & B

\end{array}

$$

I keep getting = B not A.

Note that, \[(A\cup B)\cap (B^c\cup B)=(A\cup B)\cap V=(A\cup B)\] where \(V\) is the universal set.

Kind Regards,

Sudharaka.