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Question

For any three sets $A subscript 1 end subscript comma A subscript 2 end subscript comma A subscript 3 end subscript comma$ let $B subscript 1 end subscript equals A subscript 1 end subscript comma B subscript 2 end subscript equals A subscript 2 end subscript minus A subscript 1 end subscript$ and $B subscript 3 end subscript equals A subscript 3 end subscript minus open parentheses A subscript 1 end subscript union A subscript 2 end subscript close parentheses comma$ then which one of the following statement is always true

$A_{1} \cup A_{2} \cup A_{3} \supset B_{1} \cup B_{2} \cup B_{3}$
$A_{1} \cup A_{2} \cup A_{3} = B_{1} \cup B_{2} \cup B_{3}$
$A_{1} \cup A_{2} \cup A_{3} \subset B_{1} \cup B_{2} \cup B_{3}$
None of these

The correct answer is: $A subscript 1 end subscript union A subscript 2 end subscript union A subscript 3 end subscript superset of B subscript 1 end subscript union B subscript 2 end subscript union B subscript 3 end subscript$

We have,
$B subscript 1 end subscript equals A subscript 1 end subscript rightwards double arrow B subscript 1 end subscript subset of A subscript 1 end subscript$
$B subscript 2 end subscript equals A subscript 2 end subscript minus A subscript 1 end subscript rightwards double arrow B subscript 2 end subscript subset of A subscript 2 end subscript$
$B subscript 3 end subscript equals A subscript 3 end subscript minus left parenthesis A subscript 1 end subscript union A subscript 2 end subscript right parenthesis rightwards double arrow B subscript 3 end subscript subset of A subscript 3 end subscript$
$therefore B subscript 1 end subscript union B subscript 2 end subscript union B subscript 3 end subscript subset of A subscript 1 end subscript union A subscript 2 end subscript union A subscript 3 end subscript$

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