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Maths-

General

Easy

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

Related Questions to study

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parallel

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parallel

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The shaded region in the figure represents

The shaded region in the figure represents
Maths-General

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Which of the following is/are true?

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The relation $R equals left curly bracket open parentheses 11 close parentheses comma open parentheses 22 close parentheses comma open parentheses 33 close parentheses comma open parentheses 12 close parentheses comma open parentheses 23 close parentheses comma left parenthesis 13 right parenthesis right curly bracket$ on set $A equals left curly bracket 12 comma 3 right curly bracket$ is

parallel

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