Hey, I'm currently constructing some simple proofs as an exercise, I was wondering if someone from TSR could give me a hand with them.
This is the first one, I will probably put more up.
Code:Theory: A/(A/B)=B/(B/A) Proof: Let x∊A/(A/B) then x∊A and x∉A/B, therefore x∊ and (x∉A or x∊B). Using the dissociative law we have two cases to consider either x∊ A and x∉A which leads to a contradiction so we need not consider it, or x∊A and x∊B. If x∊A and x∊B then x∉B/A. As x∊B and x∉B/A then x∊B/(B/A) and thus A/(A/B)⊆B/(B/A). Conversely let y∊B/(B/A) then y∊B and y∉B/A. Therefore we can once again reach the conclusion that y∊B and y∊A. Therefore y∉A/B and further y∊A/(A/B) and thus we conclude B/(B/A)⊆A/(A/B) as required.
Need some help with simple proofs watch
- Thread Starter
- 29-09-2010 20:04
- 29-09-2010 20:20