DOUBT IN SET THEORY

Let

M = people who have lived in Mumbai

D = people who have lived in Delhi

Total people = 80

Given:

Never lived in Mumbai = 32 ⇒ |M| = 80 − 32 = 48

Never lived in Delhi = 56 ⇒ |D| = 80 − 56 = 24

Also given:

People who have lived in both Mumbai and Delhi = 2 × (people who have only lived in Delhi)

Let only Delhi = x

Then both = 2x

Now,

|D| = (only Delhi) + (both)

24 = x + 2x

x = 8 ⇒ both = 16

Now apply union formula:

|M U D| = |M| + |D| − |M Intersection D|

= 48 + 24 − 16

= 56

People who have never lived in Delhi or Mumbai

= 80 − 56

= 24