Discrete Math - Use induction to prove. The city of Inductionapolis has multiple police districts. Any two districts are connected by a one-way street. Show that there is a route that passes through every district of the city. Solution Base case: 2 districts Since there are one-way streets between any two districts. So there is a route passing through the two districts Hence base case is true Inductive hypothesis: Assume it is true for some n number of districts, n>=2 Inductive step: We show it is true for n+1 COnsider any arbitrary district , say, D Remaining n district have a route,R, passing through them because of inductive hypothesis So, the C be a district which is the end point . Since there is a one way street from C to D call it , S So the route, R+S is the route passing through all n+1 districst Hence true for n+1 And hence for all n>=2.

1. Discrete Math -
Use induction to prove. The city of Inductionapolis has multiple police districts. Any two
districts are connected by a one-way street. Show that there is a route that passes through every
district of the city.
Solution
Base case: 2 districts
Since there are one-way streets between any two districts. So there is a route passing through the
two districts
Hence base case is true
Inductive hypothesis: Assume it is true for some n number of districts, n>=2
Inductive step: We show it is true for n+1
COnsider any arbitrary district , say, D
Remaining n district have a route,R, passing through them because of inductive hypothesis
So, the C be a district which is the end point . Since there is a one way street from C to D call it ,
S
So the route, R+S is the route passing through all n+1 districst
Hence true for n+1
And hence for all n>=2