First answer is yes. This is a good representation of the sentence, Sam has two jobs. It says there exists an x and y. One of them is a job of Sam. The other one is a job of Sam. And crucially, we have to say that x is not equal to y. Otherwise, this will be satisfied and we can have the same job represented by the variables x and y. Is this is a good representation of the member function? No, it does do a good job of telling you what is a member. So, if x is a member of a set because it’s one member, then we can always add other members, and it’s still a member of that set. But it doesn’t tell you anything about what x is not a member of. So, for example, we want to know that 3 is not a member of the empty set. But we can’t prove that with what we have here. And we have a similar problem down here. This is not a good representation of the adjacent relation. So it will tell you, for example, that square(1,1) is adjacent to square(2,1). And also to square(1,2), so it’s doing something, right? But one problem is that it doesn’t tell you any other direction. It doesn’t tell you that (2,1) is adjacent to (1,1). And another problem is that it doesn’t tell you that (1,1) is not adjacent to (8,9), because again there is no way to prove the negative. And moral is that when you try to do a definition like adjacent or member, what you usually want to do is half a sentence with the equivalent, or bi-conditional sign to say, this is true if and only if, rather than to just have an assertion, or to have an implication in one direction.