If n (P) = 5, n(Q) = 12 and n(PUQ) = 14 then n(P∩Q) =
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    7
Correct answer is option 'A'. Can you explain this answer?

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Answers

User2408930
Jul 08, 2018
Given n(P)=5 n(Q)=12 n(P union Q)=14 n((P intersection Q ) =? n(P union Q)=n(P)+n(Q)-n(P intersection Q) 14=5+12-n(P intersection Q) 14=17-n(P intersection Q) 17-14=n(P intersection Q) 3=n(P intersection Q)

Learners Habitat
Feb 18, 2022
n (P) = 5, n(Q) = 12 and n(PUQ) = 14
n(PUQ) = n(P) + n(Q) - n(P∩Q) 
14 = 5 + 12 + - n(P∩Q)
n(P∩Q) = 3

Kusum Kumari
Jul 13, 2018
It is given that n(P) = 5 n(Q) = 12 n(PUQ)= 14 then n (P intersection Q) = ? Solution :- n (PU Q) = n( P) + n (Q) - n ( P intersection Q) 14 = 5 + 12 - n( P intersection Q) 14 = 17 - n ( P intersection Q) n (P intersection Q) = 17-14 = 3

Aman Aggarwal
Jul 09, 2018
N(PUQ)=14. .............. (1) n(P)=5. .............. (2) n(Q)=12. ...............(3) n(PUQ)=n(P)+n(Q) - n(P intersection Q) from (1),(2), and (3):- 14=12+5-n(P intersection Q) 14 - 17 = - n(P intersection Q) --3= -- n(P intersection Q) 3= n(P intersection Q) n(P intersection Q)= 3

Given n(P)=5 n(Q)=12 n(P union Q)=14 n((P intersection Q ) =? n(P union Q)=n(P)+n(Q)-n(P intersection Q) 14=5+12-n(P intersection Q) 14=17-n(P intersection Q) 17-14=n(P intersection Q) 3=n(P intersection Q)
Given n(P)=5 n(Q)=12 n(P union Q)=14 n((P intersection Q ) =? n(P union Q)=n(P)+n(Q)-n(P intersection Q) 14=5+12-n(P intersection Q) 14=17-n(P intersection Q) 17-14=n(P intersection Q) 3=n(P intersection Q)