Equality operators are transitive: If A=B, and B=C, then A=B=C so A=C.
Equality operators are reflexive: A=A, B=B, and C=C no matter what their values are.
Equality operators are symmetric. If A=B, then B=A. (It doesn't matter what order they are in.)
Now, taking a look at the definition they gave you:
A tree is equal to another tree if the children are equal. Let's see. We can assume that the nodes are being compared at the bottom, or else the definition is pretty useless. But they don't bother to tell you how to resolve that comparison, and the whole definition they gave you hinges on it.
In short, it's a crappy question.
Let's see what happens if we decide we want to try and unravel the question, though.
But wait, they also tell you that the two children of any tree can be swapped. This adds the constraint that any tree that is equal to anything else (including itself) must be equal to its mirror image. And any variations of its subtrees' children being swapped.
And remember that this is supposed to be a search tree. Therefore, we can probably assume that two different search trees that are processed by the same algorithm must give the same result if they are equal. So, if we switch around the elements of a tree, then the search time would be affected. So, trees that do not have every node in place are not equal to each other.
Putting that together with the "swappable" property of this equality, we can see it's not a valid definition of equality. (If we try to apply it, then it turns out that only trees that have the same node for every node at a particular level are equal, and only to themselves, which breaks the reflexivity part of an equality operator.)
