Answer to Question #107024 in Discrete Mathematics for Shishir

Question

in a village, 180 houses have TV, 120 houses have radio. 80 houses have both. 125 houses have nothing. Find total number of houses

Answer 1

Solution. A set of houses who have a TV include a set of houses who have a TV and radio. Therefore, a set of houses who have only a TV

$$180-80=100$$

A set of houses who have a radio include a set of houses who have a TV and radio. Therefore, a set of houses who have only a radio

$$120-80=40$$

It has four sets that do not have common elements since the conditions for including elements in sets are mutually exclusive. (houses who have only a TV; houses who have only a radio; houses have nothing; houses have both TV and radio).

Therefore the total number of houses is equal to

$$100+40+125+80=345$$

Answer. 345 houses