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### Lesson 21

Laws of detachment and syllogism

Deductive reasoning

- Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties

When 2 related statements are true, deductive reasoning can be used to make a conclusion

- Foe example:
- The bakery makes fresh bread every morning.
- It is morning.
- Therefore, the bakery is making fresh bread

Using deductive reasoning

- All of Martha’s children have blue eyes. Blaine is Martha’s son.
- Therefore______________________________
- Simone wears blue and red on game days. Today is game day.
- Therefore ___________________________________
- To check out a book from the library, you must have a library card. Alex checked out a book from the library.
- Therefore ___________________________________

Law of detachment

- For 2 statements p and q,
- when “ if p, then q” is a true statement and p is true, then q is true
- We use the Law of Detachment to draw valid concluding statements.
- When the given facts are true, then correct logic can lead to a valid conclusion

caution

- Be sure to draw conclusions that are based on the information given. Do not make assumptions that are not logically sound or which have not been stated in the question

Using the law of detachment

- When it is cold outside I wear my warm jacket. It is cold outside today.
- Therefore_____________________________
- If an angle is acute, then it cannot be obtuse.. Angle D is acute.
- Therefore ________________________________
- I get paid every Friday. Today is Friday.
- Therefore_____________________________

Law of syllogism

- When “If p , then q” and
- If q , then r” are true statements, then “If p, then r” is a true statement

The Law of Syllogism is another form of deductive reasoning.

- In this case, a third conditional statement is based on 2 conditional statements in which the conclusion of one is the hypothesis of the other

Using law of syllogism

- If the wind blows from the North, then the temperature will drop. If the temperature drops, then Joe will need to wear a jacket.
- Therefore if the wind blows from the North, then _______________
- If I oversleep tomorrow morning, then I will miss my ride to school. If I miss my ride to school, then I will get a detention.
- Therefore, if I oversleep tomorrow morning, then ________________

Drawing valid conclusions

- Ten dimes are worth one dollar. One dollar is worth 100 cents.
- Therefore ____________________________________
- This is the Law of _____________________
- A car requires an oil change every 3000 miles. Jane’s car has been driven 9000 miles since its last oil change.
- Therefore ____________________________
- This is the Law of ____________________________

Draw a valid conclusion and identify the law used

- If Maria wants to see a movie, then she goes to the theater. If Maria goes to the theater, then she buys popcorn.
- Conclusion:_______________
- Law:_______________
- If it is raining then I will take an umbrella. Today it is raining.
- Conclusion:___________________________
- Law:_____________________________________

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