If A = {0, 1, 2, 3, …….., 8}, B = {3, 5, 7, 9, 11} and C = {0, 5, 10, 20}, find

Options

A. (i) A ∪ B
B. (ii) A ∪ C
C. (iii) B ∪ C
D. (iv) A ∩ B

Explanation

Let the set of people having injuries in eyes, arms or legs be denoted by E, A and L, respectively. Then, according to the problem, we have
`n(EuuAuuL)=30,n(E)=30`
`n(A)=50,n(L)=70`
and `n[(EnnAnnL')uu(EnnA'nnL)uu(E'nnAnnL)=44`
or `n(EnnAnnL')+n(EnnA'nnL)+n(E'nnAnnL)=44` [`because` each case is mutually exclusive]
or `n(EnnA)-n(EnnAnnL)+n(EnnL)-n(EnnAnnL)+n(EnnL)-n(EnnAnnL)=44`

`impliesn(EnnA)+n(EnnL)+n(AnnL)-3n(EnnAnnL)=44" ... (i)"`
`because n(EuuAuuL)=100`
`therefore n(E)+n(A)+n(L)-n(EnnA)-n(AnnL)-n(EnnL)+n(EnnAnnL)=100`
`implies30+50+70-{44+3n(EnnAnnL)}+n(EnnAnnL)=100` [from Eq. (i)]
`implies 6-2n(EnnAnnL)=0`
`therefore n(EnnL nnA)=3`
Hence, there are three claims involved in loss or injury to all the three.