Give a formal proof that A = B:
Let A be the set of all dogs bred to hunt badgers
Let B be the set of all dogs who are Dachshunds
Now use the following "facts" to give a formal proof that A = B (Hint: remember you must prove two separate things). The "facts" are:
(1) If a dog is bred to hunt badgers, then the dog is good at digging
(2) If a dog is good at digging, then the dog is a Dachshund
(3) If a dog is a Dachshund, then the dog is good at digging
(4) If a dog is good at digging, the dog is bred to hunt badgers