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I'm watching a video on coursera (thinking mathematically course) and one of the questions from the disjunction section was:

Let $A$ be the sentence "It will rain tomorrow". Let $B$ be the sentence "It will be dry tomorrow".

Does $A \vee B$ accurately reflect the meaning of the sentence: "Tomorrow it will rain OR it will be dry all day"?

I thought the answer was yes, but I was wrong!

Can someone please explain why the answer is no?

user2669338
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  • @DanPiponi yes I realized my mistake that's why I eliminated the comment ;) – Fede Poncio Dec 18 '15 at 01:28
  • For what it's worth, I think this is a bad example - at first glance I read the question as "Tomorrow [it will rain OR (it will be dry all day)]", and "it will be dry" (B) as "it will be dry all day" (on the grounds that it's kind of silly to say "It was dry on Tuesday, except for that rainstorm" :P) - so my first instinct was yes, as well. The inclusive vs. exclusive issue is important, but don't feel bad OP - this particular case was pretty ambiguous. – Noah Schweber Dec 19 '15 at 05:33
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    @NoahSchweber it's good to know I'm not the only one who was thrown off by the wording. Thanks for the clarification. – user2669338 Dec 19 '15 at 11:32

1 Answers1

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The "all day" clause is the key point.   That makes it an exclusive-or statement.

$A\vee B$ means "it will either rain tomorrow, be dry tomorrow, or both".   It's an inclusive-or statement.   (For example: It can be dry in the morning, and rain in the evening.)

Graham Kemp
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