Im trying to solve this problem from Dummit & Foote:
Let $G$ be a transitive permutation group on the finite set $A$. A block is a nonempty subset $B$ of $A$ such that for all $\sigma\in G$ either $\sigma(B)=B$ or $\sigma(B)\cap B=\emptyset$ (here $\sigma(B)$ is the set $\{\sigma(b)|b\in B\}$).
(c) A (transitive) group G on a set A is said to be primitive if the only blocks in A are the trivial ones: the sets of size 1 and A itself. Show that S4 is primitive on A={1,2,3,4}. Show that D8 is not primitive as a permutation group on the four vertices of a square
In part (c) i have to show that the subsets are {1,2} and {1,2,3} are not blocks, but im confused with the operation that i need to perform, namely:
(13){1,2},
(34){1,2,3}
I know that the answers are: (13){1,2} = {1,3} and (34){1,2,3} = {1,2,4}, but i don't understand the procedure.