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Associative Law of Binary Operation

Two sets are ...

Question

Two sets are given as $X = {10, 11, 12, 13}$ and $Y = {2, 3, 4, 6, 12, 18, 36},$ then $X \cup Y =$

A

X

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B

Y \cup X

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C

{2, 3, 4, 6, 10, 11, 12, 13, 18, 36}

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D

Y

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Solution

The correct option is C ${2, 3, 4, 6, 10, 11, 12, 13, 18, 36}$
Given $X = {10, 11, 12, 13}$ and $Y = {2, 3, 4, 6, 12, 18, 36}$
Now, $X \cup Y = {10, 11, 12, 13} \cup {2, 3, 4, 6, 12, 18, 36}$
$\Rightarrow X \cup Y = {2, 3, 4, 6, 10, 11, 12, 13, 18, 36}$
Also, we know from commutative law, $X \cup Y = Y \cup X$

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