Proving a symmetric group is a subgroup

Question

Warning: This is a homework question. I only need help on understanding the set.

Question: Suppose $n>2$ Is $H$ a subgroup of $S_n$

$H=\{f \in S_n : f \bullet 1=1 $ and $f \bullet 2=2\} $

My problem for being unable to answer the question is that I am struggling to understand how the word "and" affects the question. In terms of proving/disproving it I would proceed with the sub-group test.

Answer 1

The question is asking, "If you look at all permutations of $n$ items (i.e., $S_n$), there are some that leave the items 1 and 2 fixed. Call the set of those $H$. Is it a subgroup of $S_n$ or not?"

For $S_4$, the set $H$ consists of

1. The identity permutation, and
2. The permutation that swaps items 3 and 4.