For all sets A and B, (A - B) (A B) = A - Vidyadip

Question

For all sets A and B, $(\text{A} - \text{B}) \cup (\text{A} \cap \text{B}) = \text{A}$

✓

Answer

True.
$\text{L.H.S.}=(\text{A}-\text{B})\cup(\text{A}\cap\text{B})$
$=\big[(\text{A}-\text{B})\cup\text{A}\big]\cap[(\text{A}-\text{B})\cup\text{B}\big]$
$=\text{A}\cap(\text{A}-\text{B})=\text{A}=\text{R.H.S.}$
$\text{L.H.S.}=\text{R.H.S.}$
Hence, given statement is true.

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