Composition relation of P∘P

Question

Consider the following relation P on the set B = {a, b, {a, b}}:

P = {(a, a), (a, b), (b, {a, b}), ({a, b}, a)}.

Answer questions 6 to 8 by using the given relation P.

Question 6 Which one of the following alternatives represents the domain of P (dom(P))?

1. {a, b}
2. {{a, b}}
3. a, b, {a, b}
4. {a, b, {a, b}}

Question 7 Which one of the following relations represents the composition relation P ○ P?

1. {(a, a),(a, b), (a, {a, b}), (b, a)}
2. {(a, a),(a, b), (a, {a, b}), (b, a), ({a, b}, a), ({a, b}, b)}
3. {(a, a),(a, b), (b, a)}
4. {(a, a),(a, b), (b, a), ({a, b}, {a, b})}

Question 8 The relation P is not transitive. Which ordered pairs can be included in P so that P would satisfy transitivity?

1. (a, {a, b}) & (b, a)
2. (b, b) & ({a, b}, {a, b})
3. (b, a), (b, b), (a, {a, b}), ({a, b}, b) & ({a, b}, {a, b})
4. (b, a), (a, {a, b}) & ({a, b}, b)