Question

A survey was conducted among 1000 people of these 595 are democrats, 595 wear glasses and 550 like ice cream. 395 of them are democrats who wear glasses. 350 of them are democrats who like ice cream and 400 of them are wear glasses and like ice cream. 250 of them are democrats and wear glasses and like ice cream. How many of them who are not democrats, do not wear glasses and do not like ice cream? How many of them who are democrats do not wear glasses and do not like ice cream?

Answer 1

Answer:

Step-by-step explanation:

Given  

A survey was conducted among 1000 people of these 595 are democrats, 595 wear glasses and 550 like ice cream. 395 of them are democrats who wear glasses. 350 of them are democrats who like ice cream and 400 of them are wear glasses and like ice cream. 250 of them are democrats and wear glasses and like ice cream. How many of them who are not democrats, do not wear glasses and do not like ice cream? How many of them who are democrats do not wear glasses and do not like ice cream?

Given X = 1000

Let D be number of democrats.

So D = 595

Let G be number of people who wear glasses.

So G = 595

Let I be number of people who like icecream.

So I = 550

Now D ∩ G = 395

Also D ∩ I = 350

G ∩ I = 400

So D ∩ G ∩ I = 250

Now D Ս G Ս I = D + G + I – (D ∩ G) + ( G ∩ I) + (D ∩ G) + (D ∩ G ∩ I)

                         = 595 + 595 + 550 – (395 + 350 + 400) + 250

                       = 845

Now 845 are either Democrats or wear glasses or like ice cream.

So 1000 – 845 = 155

Now 155 people are neither Democrats nor wear glasses nor like ice cream.

Number of people who are Democrats do not wear glasses and do not like ice cream

        = D – (D ∩ G) – (D ∩ I) + (D ∩ G ∩ I)

        = 595 – (395 + 300) + 250

         = 845 – 695

        = 150