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Set theory

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Among $150$ faculty members in an institute, $55$ are connected with each other through Facebook ${ }^{\circledR}$ and $85$ are connected through WhatsApp ${ }^{\circledR}. 30$ faculty members do not have Facebook ${ }^{\circledR}$ or WhatsApp ${ }^{\circledR}$ accounts. The number of faculty members connected only through Facebook ${ }^{\circledR}$ accounts is _______

  1. $35$
  2. $45$
  3. $65$
  4. $90$

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Total no of people connected either one of them :  $150 - 30 =120 $
Total people connected= People connected through $ \ Whatsapp + \  Facebook \  - (\ Whatsapp \bigcap \ Facebook) $
$120 = 55 + 85 - X \\ X=20 \\ \therefore Only \ through \ facebook = 55-20 = 35$
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