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Maths-

General

Easy

Question

If $a blank N equals left curly bracket a blank x blank colon x element of N right curly bracket$ and $b blank N blank intersection c blank N equals d blank N comma$ where $b comma c element of N$ are relatively prime, then

$d = b c$
$c = b d$
$b = c d$
None of these

The correct answer is: $d equals b c$

We have,
$b blank N equals open curly brackets b blank x vertical line x element of N close curly brackets equals$ Set of positive integral multiples of $b$
$c blank N equals open curly brackets c blank x vertical line x element of N close curly brackets equals$ Set positive integral multiples of $c$
$therefore b N intersection c N equals$ Set of positive integral multiples of $b c$
$rightwards double arrow b N intersection c N equals b c blank N$ [ $because b$ and $c$ are prime]
Hence, $d equals b c$

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