Sets and relations

answers

1) 420

2) 220

3) 220

De Morgan’s law

n(A u B u C) = n(A) + n(B) + n(C) - n(A n B ) -  n(B n C) - n(A n C) + n (A n B n C)

n(C u T u S) = n(C) + n(T) + n(S) - n(C n T) -  n(T n S) - n(C n S) + n (C n T n S)   -------- (1)

n(C) = 960

n(T) = 1080

n(S) = 1280

n(C n T) =  560

n(T n S) = 640

n(C n S) = 600

n(C ^c n T ^c n S ^c) = 60

n(C ^c n T ^c n S ^c) = n(C  u T  u S) ^c

total number of employees = n(C u T u S) + n(C u T u S) ^c ------------------------------(2)

substitute values in eqn (1) & (2), we get

2000 = 960 + 1080 + 1280 – 560  - 640 - 600 + n (C n T n S)    + 60

n (C n T n S)    = 2000 – 1580

the number having all three, n (C n T n S)   =  420

2) no of emoployees having t & s    but not c =

n(T n S) - n (C n T n S) = 640- 420

= 220

3) no of preferring coffee only =

n(C) - n(C n T) - n(C n S) + n (C n T n S) = 960 – 560 – 600 + 420

 = 220

venn diagram for more explanation