If Iris is scheduled for the next day after Harry, which one of the following lists all those days any one of which c...
BaylorNovember 22, 2019
question about the rules
This isn't a question about this problem but I'm curious, if Nancy is scheduled for Friday can we automatically conclude harry is on Monday if a problem had that scenario? How is it possible to know when you can make that deduction because sometimes I see examples where you can make that deduction and I've seen other times where it would be wrong to just assume for example harry is on Monday just because Nancy is Friday. Im sure its all about the wording but could you possibly word it in a way for me to see an example of where Nancy could be on Friday and it wouldn't mean that harry had to be on Monday. Thanks
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No, we cannot conclude anything about Harry's schedule just because Nancy is scheduled for Friday, this is a fallacy of mistaken reversal and would be a wrong inference to make in any scenario. We must apply the rules of inference when making any deductions from the rules. The rule tells us that if Harry is scheduled for Monday, then Nancy is scheduled for Friday.
To find a contrapositive - a logically equivalent statement - we need to reverse and negate both sides of the conditional statement. This means that we can only infer that:
If Nancy is not scheduled for Friday, then Harry is not scheduled for Monday.
If Nancy is scheduled for Friday, it could be true that Harry is scheduled for Monday or he could be scheduled for any other day. This rule does not constrain Harry's placement when Nancy is scheduled for Friday.
Let me know if this makes sense and if you have any further questions.
BaylorNovember 22, 2019
thank you makes sense
RaviNovember 29, 2019
@baylor, let us know if you have any other questions!
rinavalerianoApril 5, 2020
For the contrapositive used in this example. If Nancy is not scheduled Friday then Harry can not be scheduled for Monday. Does this for example mean that if Nancy is scheduled Wednesday (or any day not Friday), then we can conclude Harry will not be scheduled Monday?
SkylarMay 2, 2020
@rinavaleriano, happy to help!
Yes, that is correct.
We are told: If Harry is scheduled for Monday, Nancy is scheduled for Friday. We can diagram this as: H(M) -> N(F) The contrapositive is: NOT N(F) -> NOT H(M)
So, if Nancy is NOT scheduled for Friday (AKA she is scheduled Monday, Tuesday, Wednesday, or Thursday), then Harry must NOT be scheduled for Monday (AKA he must be scheduled Tuesday, Wednesday, Thursday, or Friday instead). This is because all contestants must be scheduled once Monday through Friday.
Does that make sense? Please let us know if you have any other questions!
