Question

Show that if every room in a house has an even number of doors, then the number of outside entrance doors must be even as well.

a) True
b) False

Answer 1

The statement is true; the number of outside entrance doors must be even if every room has an even number of doors, as shown by graph theory and Euler's theorem.

Step-by-step explanation:

The statement that the number of outside entrance doors must be even if every room in a house has an even number of doors is indeed true. This can be demonstrated using the concept of graph theory in mathematics, specifically Euler's theorem. Visually, each room can be seen as a vertex in a graph and every door as an edge. An even number of doors in every room implies an even degree for every vertex. A graph with all vertices of even degree must have an even number of edges leaving the graph (outside doors), thus the number of outside entrance doors is even.