Question

At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture?

Answer 1

The number of women teachers attending the lecture is 1.

Explanation:

Denote the variables as follows:

M = men

W = women

T = teacher

The data provided is:

n (M) = 23

n (W) = 29

n (T) = 4

n (M ∪ T) = 24

Compute the number of men teachers as follows:

`n(M\cap T)=n(M)+n(T)-n(M\cup T)`

`=23+4-24\\=3`

Compute the number of women teachers as follows:

`n(T)=n(M\cap T)+n(W\cap T)`

`4=3+n(W\cap T)`

`n(W\cap T)=1`

Thus, the number of women teachers attending the lecture is 1.