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Law of Detachment and Law of Syllogism

- Math 2 - Lesson 4
- Mr. Lopez

Do Now

- Write in symbolic form the following converse,

inverse and contrapositive for the following

sentence. - p ?? r
- Express a sentence logically equivalent to the

following sentence. - r ?? q

Converse r ? p Inverse p ? r Contrapositive

r ? p

Contrapositive q ? r

Law of Detachment

- If a conditional sentence is true and if the

hypothesis of the conditional is also true then,

the conclusion must also be true. - If p ? q is true, and p is true, then q must also

be true.

Using the Law of Detachment

- Based on the two given statements, what can be

concluded by using the Law of Detachment? - If M is the midpoint of a segment, then it

divides the segment into two congruent segments.

(True) - M is midpoint of AB. (True)
- By using the Law of Detachment, we can conclude

that M divides AB into two congruent segments of

AM MB

Using the Law of Detachment

- However, not all sentences can be determined with

the Law of Detachment. - Example 1
- After using the Law of Detachment is the

conclusion true? - Given
- If it is snowing, then the temperature is less

than or equal to 32 degrees. (True) - The temperature is 20 degrees. (True)
- Conclusion
- It must be snowing.
- THIS IS NOT ALWAYS TRUE. IT CAN BE LESS THAN 20

DEGREES AND NOT SNOW!

Using the Law of Detachment

- Example 2
- Given
- If a road is icy, then the driving conditions

are hazardous. (True) - Driving conditions are hazardous. (True)
- Conclusion
- NO CONCLUSION CAN BE MADE BECAUSE WE DONT KNOW

IF THE HYPOTHESIS (ICY ROAD) IS TRUE OF FALSE.

Law of Syllogism

- If p ? q is true and
- q ? r is true then
- p ? r is true.
- This law is similar to the transitive property in

algebra - If a b and b c then a c

Using the Law of Syllogism

- Example
- Given
- If a number is prime then it doesnt have

repeated factors. (True) - If a number doesnt have repeated factors, then

it is not a perfect square. (True) - According to the Law of Syllogism, we can

conclude that - If a number is prime, then it is not a perfect

square.

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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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