GATE | GATE-CS-2016 (Set 2) | Question 6
Among 150 faculty members in an institute, 55 are connected with each other through Facebook ® and 85 are connected through WhatsApp ® . 30 faculty members do not have Facebook ® or WhatsApp ® accounts. The number of faculty members connected only through Facebook ® accounts is ______________.
n(F) : number of faculty connected through facebook
n(W) : number of faculty connected through whatsapp
n(F ∪ W) : number of faculty connected through either facebook and whatsapp
n(F ∩ W) : number of faculty connected through both facebook and whatsapp
n(F ∪ W) = (total faculty – faculty not connected to anything) = (150-30) = 120
From number theory:
n(F ∪ W) = n(F) + n(W) – n(F ∩ W)
n(F) – n(F ∩ W) = n(F ∪ W) – n(W)
n(F) – N(F ∩ W) = (120-85) = 35
n(F)- n(F ∩ W) is the faculty that has only facebook account, Hence answer is 35.
This explanation has been contributed by Dharmesh Singh.
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