Answer to Question #107024 in Discrete Mathematics for Shishir

Question #107024
in a village, 180 houses have TV, 120 houses have radio. 80 houses have both. 125 houses have nothing. Find total number of houses
1
Expert's answer
2020-03-31T07:19:00-0400

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


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