7. Agatha, Isa, and Nick each have a different type of bicycle. One of them has an electric bike, one has a racing bike, and one has a mountain bike. The bikes each have a different color: green, blue, or black. Each of the three owners makes two statements, one of which is true and one is false:

- Agatha says: "I have an electric bike. Isa has a blue bike."
- Isa says: "I have a mountain bike. Nick has an electric bike."
- Nick says: "I have a blue bike. The racing bike is black."

Exactly one of the following statements is certainly true. Which one?
A) Agatha has a green bike.
B) Agatha has a mountain bike.
C) Isa has a green bike.
D) Isa has a mountain bike.
E) Nick has an electric bike.
A7. D) Isa has a mountain bike.

Suppose Isa does not have a mountain bike. Then the other statement by Isa must be true, and Nick has the electric bike. So Isa has neither the mountain bike nor the electric bike, which means she has the racing bike. Since Nick has the electric bike, the first statement by Agatha is false; the second one is therefore true, which means we now even know the color of Isa's racing bike: blue. But then both statements by Nick are false; contradiction. So Isa must have the mountain bike. Therefore, D) is at least true.

In the following two situations, exactly one statement is true for each of the three cyclists. These are thus two situations that can occur, from which it follows that the claims in A), B), C), and E) are not true in all possible situations.

| Agatha | electric bike | green | Agatha | electric bike | black |
| :--- | :--- | :--- | :--- | :--- | :--- |
| Isa | mountain bike | black | Isa | mountain bike | green |
| Nick | racing bike | blue | Nick | racing bike | blue |