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Logical Arguments A logical argument is made up of premises (assumptions, laws, rules, widely held ideas, or observations) and a conclusion 3.5 – Analyzing Arguments with Euler Diagrams Valid and Invalid Arguments An argument is valid if the fact that all the premises are true forces the conclusion to be true. Arguments with Universal Quantifiers Several techniques can be used to check the validity of an argument. One visual technique is based on Euler Diagrams. An argument that is not valid is invalid. It is called a fallacy.

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Using an Euler Diagram to Determine Validity Is the following argument valid? All cats are animals. Fuzzy is a cat. Fuzzy is an animal. 3.5 – Analyzing Arguments with Euler Diagrams Animals Cats x represents Fuzzy. x The diagram shows that Fuzzy is inside the region for animals. The argument is valid.

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Using an Euler Diagram to Determine Validity Is the following argument valid? All sunny days are hot. Today is not hot Today is not sunny. 3.5 – Analyzing Arguments with Euler Diagrams Sunny days x Hot days x represents today The diagram shows that today is outside the region for sunny. The argument is valid.

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Using an Euler Diagram to Determine Validity Is the following argument valid? All cars have wheels. That vehicle has wheels. That vehicle is a car. 3.5 – Analyzing Arguments with Euler Diagrams Things that have wheels Cars x represents that vehicle x ? The diagram shows that vehicle can be inside the region for Cars or outside it. The argument is invalid.

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Using an Euler Diagram to Determine Validity Is the following argument valid? Some students drink coffee. I am a student. I drink coffee. 3.5 – Analyzing Arguments with Euler Diagrams People that drink coffee Students I ? The diagram shows that I can be inside the region for Drink coffee or outside it. The argument is invalid.

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Use an Euler Diagram with quantifiers such as: all, some, every, no, etc. Is the following argument valid? If the day is sunny, then it is hot. Today is not hot Today is not sunny. 3.6 – Analyzing Arguments with Truth Tables q: it is hot Use a Truth Table if the argument does not contain any quantifiers. p: if the day is sunny p: if the day is not sunny q: it is not hot

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Is the following argument valid? If the day is sunny, then it is hot. Today is not hot Today is not sunny. 3.6 – Analyzing Arguments with Truth Tables q: it is hot p: if the day is sunny p: if the day is not sunny q: it is not hot p q q p pq p q T (p q) q((p q) q) p T F F T F T F F F T T F T F T T F T T F F F T T T T T Tautology Valid Argument

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Is the following argument valid? I will go to the fair or I will go to the beach. I did not go to the fair. I went to the beach. 3.6 – Analyzing Arguments with Truth Tables q: I go to the beach p: I go to the fair p: I do not go to the fair q: I do not go to the beach. p q p q pq p T (p q) p((p q) p) q T F F T F T F F F T T T T T F F F T F T T T T Tautology Valid Argument

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Is the following argument valid? If you go to the jungle, you will see a tiger. You did not go to the jungle. You did not see a tiger. 3.6 – Analyzing Arguments with Truth Tables q: will see a tiger p: go to the jungle p: do not go to the jungle q: will not see a tiger p q p q pq p q T (p q) p((p q) p) q T F F T F T F F F T T F T F T T F T T F F T T T T F T Not a tautology Invalid Argument

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