Translate the following inference to logic notation: For all x, x_7 will make tea. There is at least one x for which if x_7 cooks, then x_7 is bored. For all x, x_7 will make tea if and only if x_7 will cook. Therefore there is at least one x for which x_7 is bored.
forall x: P(x). exists x: Q(x) -> R(x). forall x: P(x) <-> Q(x). Therefore exists x: R(x).