Translate the following inference to logic notation: Michael is climbing a mountain if and only if it is cloudy. If Mary plays a game, then it is cloudy. Mary is playing a game if and only if Mary is a bartender. If Michael climbs a mountain, then Mary is a bartender. Therefore it is cloudy if and only if Michael is climbing a mountain.
p <-> q. r -> q. r <-> s. p -> s. Therefore q <-> p.