# Let A and B be sets. Prove that A = B if and only if A is a set of B and B is a set of A.?

• Let A and B be sets. Prove that A = B if and only if A is a set of B and B is a set of A.?

Answer #1 | 08/02 2014 10:30
you can use Galois Theory for that.
Positive: 56 %

... Let A and B be sets. A function (mapping, map) f from A to B ... Whenever there is a bijection from A to B, the two sets ... Let E be the set ...
Positive: 56 %
Examples of Proof: Sets ... Proof: Let x ∈ A−B. By deﬁnition of set diﬀerence, x ∈ A and x 6∈B. Thus, ... Let’s prove this.
Positive: 51 %
If A is a subset of a set B, ... A → B is invertible if and only if it is a bijection. ... Let A,B and C be sets. Prove DeMorgan’s laws via element ...