We can use a Venn diagram to represent the rooms with painted walls and the rooms with ceramic tiled walls.
Let P be the set of rooms with painted walls and C be the set of rooms with ceramic tiled walls. The Venn diagram will have two overlapping circles, one for set P and one for set C.
According to the problem, we have the following information:
- |P| = 6 (6 rooms have painted walls)
- |C| = 2 (2 rooms have ceramic tiled walls)
- |P ∩ C| = 1 (1 room has both painted and ceramic tiled walls)
To find the number of rooms without either painted or ceramic tiled walls, we need to find the number of rooms outside of the two circles in the Venn diagram.
Since there is a total of 9 rooms, we can use the principle of inclusion-exclusion to find the number of rooms without either type of walls:
|P ∪ C| = |P| + |C| - |P ∩ C| = 6 + 2 - 1 = 7
Now we can find the number of rooms without either painted or ceramic tiled walls by subtracting the number of rooms with either type of walls from the total number of rooms:
9 - 7 = 2
So, there are 2 rooms that do not have either painted or ceramic tiled walls.
In a house made up of 9 rooms, 6 rooms have painted walls, 2 rooms have ceramic tiled walls and 1 room has both painted and ceramic tiled walls. How many rooms do not have either painted or ceramic tiled walls?
(Venn diagram required)
1 answer