Thread: Set Theory Proof

Prove { {a}, {a,b} } = { {c}, {c,d} } if and only if a=b and c=d.

I'm wondering how to proceed. I'm not even sure what exactly am I trying to prove

Originally Posted by TitaniumX

Prove { {a}, {a,b} } = { {c}, {c,d} } if and only if a=b and c=d.

I'm wondering how to proceed. I'm not even sure what exactly am I trying to prove

For sets A,B the definition tells us that , so:

, and so .

But contains one single element so this set cannot be equal to a set containing two elements, and thus . Take it from here.

Tonio