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1.6 Example Discrete Math
π: Show that the premises
β’ βIt is not sunny this afternoon and it is colder than yesterday,β
β’ βWe will go swimming only if it is sunny,β
β’ βIf we do not go swimming, then we will take a canoe trip,β and
β’ βIf we take a canoe trip, then we will be home by sunsetβ
lead to the conclusion βWe will be home by sunset.β
help me to solve this
π€: Of course! To help you solve this problem, I'll break down each step of the argument:
- Premise: "It is not sunny this afternoon and it is colder than yesterday."
- Conclusion: "We will go swimming only if it is sunny."
- Premise: "If we do not go swimming, then we will take a canoe trip."
- Conclusion: "If we take a canoe trip, then we will be home by sunset."
- Inference (the logical connection between the premises and the conclusion): The reason why we won't go swimming if it's not sunny is because we will take a canoe trip instead. And since taking a canoe trip means we will be home by sunset, therefore we will be home by sunset.
So, the argument leads directly from the initial premises to the conclusion.
π: use boolean operator
π€: Sure! Let's represent the argument using Boolean operators:
Premise 1: Β¬(Sunny today) β Going for swim cancelled
Premise 2: If no swimming, then Canoe trip
Premise 3: If take Canoe trip, then Home by Sunset
Conclusion: Therefore, Home by Sunset
Here's how we can connect these premises using Boolean operators:
Β¬(Sunny today) β Going for swim cancelled |β> No Swimming β Take Canoe Trip |β> Home by Sunset
In this representation, the vertical bars(|β>) indicate the conditional connections between the premises and the conclusion.
Using these Boolean operators, we can see that the argument logically follows from the given premises, leading to the conclusion that We will be home by sunset.