If aN = { ax:x ∈ N} and bN cap cN = dN , where b , c ∈ N are relatively prime, then

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1.Set Theory

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If $aN = \{ ax:x \in N\} $ and $bN \cap cN = dN$, where $b$, $c \in N$ are relatively prime, then

A

$d = bc$

B

$c = bd$

C

$b = cd$

D

None of these

Solution

(a) $bN = $ the set of positive integral multiples of b, $cN$= the set of positive integral multiplies of $c$.

$\therefore $ $bN \cap cN$= the set of positive integral multiples of $bc$
= $b \subset N$, $[ are\, prime]$

$\therefore $ $d = bc$.

Standard 11

Mathematics

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