Search code examples
logicproof

Proof from Axioms

Given the axioms

  • Henry owns a bike
  • Every bike owner loves racing
  • No one who loves racing buys a scooter.
  • Either Henry or Bob bought a scooter, which is named Bill

Did Bob buy the scooter?

This is a homework question; it seems almost too easy, so I just want to check to make sure my logic is correct.

Since either Henry or Bob bought a scooter, and since Henry owns a bike and therefore loves racing and therefore cannot buy a scooter, then Bob must have been the one to buy the scooter.

Am I correct in my logic and my answer?

Solution

  • Legend:

    Owns a bike === A
Loves racing === B
Buys a skooter === C

    Rephrase the logic conditions:

    Henry is A
A => B
B => Not(C)
Henry or Bob is C

    Calculations:

    Henry is A => Henry is B => Henry is Not(C) => Bob is C
Meaning: Bob bought a skooter

    So yes - you are correct. If it seems easy, it may be just to understand the tools you should use, to get you ready for more complex problems.