Question

2. Out of a group of 1000 people, 560 have a TV, 250 have a computer and 130 have both.
Find the number of people who have
(i) only a TV
(ii) only a computer
(iii) either a TV or a computer or both (iv) neither a TV nor a computer.

please help! ​

Answer 1

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• Let the group of people be S

Therefore,

n(S)=1000

Let the group of people having Tv be T

Therefore,

n(T)=560

Let the group of people having computer be C

Therefore,

n(C)=250

There are 130 people people having both computer and TV

Therefore,

n(TnC)=130

• 1.People having only TV.

n(T)=n(T)-n(TnC)

= 560-130

=430

• 2.People having only computer

n(C)=n(C)-n(TnC)

=250-130

=120

• 3.People having either a TV or a computer or both

Let this set be n(TuC)

n(TuC)=n(T)+n(C)-n(TnC)

=560+250-130

=810-130

1. =790---------(1)

4.People not having neither a TV nor a computer.

n(TnC)'=1000-[n(T)+n(C)-n(TnC)

=1000-790-----(from 1)

=210

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