Relations and Functions

Question

# In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Set A = set of students who know Hindi
n(A)  = 100                                                                                    .....(i)
Set B = set of students who know English
n(B)   = 50                                                                                      ....(ii)
Also,                                                                            .....(iii)
Using,
= 100 +50 - 25 = 125
All students know at least one of the two languages

Hence, the number of students in the group = 125