# Using isomorphism and permutations in proofs

#### Yuuki

##### Member
I have trouble using isomorphism and permutation in proofs for combinatorics.
I don't know when I can assume "without loss of generality".
What are some guidelines to using symmetry in arguments.

One problem I'm working on that uses symmetry is to "prove that any (7, 7, 4, 4, 2)-designs must be isomorphic."

#### Sudharaka

##### Well-known member
MHB Math Helper
I don't know when I can assume "without loss of generality".
Hi Yuuki,

Well, I don't have the background to answer all your questions but would like to clarify about statement "without loss of generality". First of all it's not an assumption but rather a way of narrowing down a proof to a special case. All the other possibilities of the proof just follows the same procedure with symbols and objects interchanged. You would find a nice example about the use of this statement >>here<<.