If $A = {b, e, f, g}$ and $B = {c, e, g, h}$ , then verify the commutative property of (i) union of set, (ii) intersection of sets

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Solution

$A = {b, c, f, g}$ , $B = {c, e, g, h}$
(i) $A c u p B = B \cup A$
$A \cup B = {b, e, f, g} \cup {c, e, g, h}$
$= {b, c, e, f, g, h}$ ………. $(1)$
$B \cup A = {c, e, g, h} \cup {b, e, f, g}$
$= {b, c, e, f, g, h}$ ………… $(2)$
$A \cup B = B \cup A$
(ii) $A \cap B = B \cap A$
$A \cap B = {b, e, f, g} \cap {c, e, g, h}$
$= {e, g}$ ………….. $(1)$
$B \cap A = {c, e, g, h} \cap {b, e, f, g}$
$= {e, g}$ ………… $(2)$
$A \cap B = B \cap A$ .

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