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:

Let M denotes men , W denotes women and T denotes teachers.

Number of women = n(W)=29

Number of men = n(M)=23

Number of teachers=n(T)=4

We are given that 24 are either men or teachers.

So,n(M∪T)=24

We are supposed to find the number of women teachers attending the lecture. ​

n(M∪T)=n(M)+n(T)-n(M∩T)

24=23+4-n(M∩T)

n(M∩T)=3

So,No. of teachers those are men is 3

Total number of teachers = 4

So, the number of women teachers attending the lecture= 4-3 = 1

Hence the number of women teachers attending the lecture is 1