SETS B16

In Bibanja district the number of people who speak Kiswahili or Lingala is 450. 200 of them speak Kiswahili and 300 of them speak Lingala. How many speak both languages?

Solution

In most cases, OR stands for union whereas AND/BOTH, stands for intersection.

Let Kiswahili=n(K), Lingala= n(L).

n(K)= 200 ,

n(L)= 300,

n(KuL) = 450,

n(KnL)=?

n(KuL) = n(K) + n(L) - n(KnL)

450  =  200 + 300 – n(KnL)

450  =  500 – n(KnL)

450 -500 = -n(KnL)

-50 = -n(KnL)

n(KnL) =  50  [after dividing by (-1) on both sides]

Hence n(KnL)=50 answer