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If it rains at night, then the next morning is always cloudy. The morning today is cloudy. Then

  • A.It must have rained last night.
  • B.It may have rained last night.
  • C.It will rain tonight.
  • D.It will not rain tonight.

Answer: B

The valid conclusion is that it may have rained last night.

The rule is 'if it rains at night, the next morning is cloudy'. A cloudy morning is the consequence, not the cause; mornings can be cloudy for other reasons. Reasoning from the consequence back to the cause ('the morning is cloudy, so it rained') is the fallacy of affirming the consequent, so it cannot be said that it must have rained. But a cloudy morning is consistent with rain, so rain last night remains possible.

The statements say nothing about tonight, so both 'It will rain tonight' and 'It will not rain tonight' are unsupported.

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