(i) From A ⇒ B to A ⇒ (B ∨ C) 
(ii) From A ⇒ B and A ⇒ C to A ⇒ (B ∧ C)
(iii) From A ⇒ B to ¬B ⇒ ¬A

Which of the preceding inferences are valid for default conditionals? If it is valid, give an argument. If it is invalid, draw a counter-model with a few situations and a plausibility relation where the premises are true while the conclusion is false. Now define a probabilistic conditional A ⇒ B as saying that the conditional probability P(B|A) > 2. Which of the preceding principles are valid for this probabilistic conditional? describe why or why not.
Discuss the main difference that you found in your answers. Can you give a crisp reason why default reasoning and probabilistic reasoning are close, but different?