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There is an example in the section 1.6 which goes as:

Show that the premises “It is not sunny this afternoon and it is colder than yesterday,” “We will  go swimming only if it is sunny,” “If we do not go swimming, then we will take a canoe trip,”  and “If we take a canoe trip, then we will be home by sunset”Show that the premises “It is not sunny this afternoon and it is colder than yesterday,” “We will  go swimming only if it is sunny,” “If we do not go swimming, then we will take a canoe trip,”  and “If we take a canoe trip, then we will be home by sunset”

In the solution the author rosen writes line which goes as:

Let p be the proposition "It is sunny this afternoon", q the proposition "It is colder than yesterday", r the proposition "We will go swimming", s the proposition "We will take a canoe trip", and the t the proposition "We will be home by sunset". Then the premises become

¬p∧q,r→p and some text.

Now my question comes here. According to the definition of conditional statement p->q means "q only if p". So, according to that definition and from above question it should p→r and not r→p. Where am i wrong? Anyone Please clear this doubt. and also if we take r->p it translates to "if we will go swimming then it is sunny" it does not make sense in any world according to me. Thanks in advance.

 

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in Mathematical Logic by (17 points) | 63 views
+1

didn't understood your question clearly, but i hope this will help you

0
yeah i was thinking that my question may not be clear. let me clarify. Yes according to the paragraph that you shared one of the meaning of the implication p->q is "q only if p". isn't it? Now in my question in the given example there is a implication r->p which i highlighted by bolding. now my main question is shouldn't it be p->r according to the defn of implication. But rosen has written r->p. So i want to confirm if i am right and if i am wrong please explain me where i am wrong. Hope this clarifies things.
0
My bad, I understood where i was wrong. I got confused between "q if p" and "p only if q". Thank you very much for taking time to help me.
0
If you got it.. then it is ok

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