Law of Detachment
In order for the law of detachment to have a valid conclusion what must be restated after the conditional statement?
Hypothesis
Law of Syllogism states:
P -> q
___ -> ___
___ -> r
q, r, p
(T/F) A biconditional is written as ___ if an only if ____
True
The Law of Detachment states:(p -> q)
(__ is true), (therefore __ is true)
a) p, q
b) q, p
a)
What is the conclusion formula under the law of syllogism?
p -> r
Is this a biconditional?
"An angle is a right angle if and only if it measures 90 degrees."
yes
Is this a valid conclusion?
If an animal is a dog, then it has four legs.
Leonard is a dog.
Therefore, Leonard has four legs.
Yes
Make this conclusion valid by filling in the blanks.
If the rainbow starts with red, then it will be orange. If orange follows, yellow will come next.
Conclusion: If the rainbow starts with _____, it will eventually lead to _______.
red, yellow
What two things make up a biconditional statement?
Conditional and converse
If it's cloudy outside, then it will rain.
The sky is cloudy. What can I conclude?
It will rain.
What is the conclusion to the following statements.
If it snows, the roads will be slippery.
If the roads are slippery, driving will be dangerous.
If it snows, driving will be dangerous.
What is the conditional from the following biconditional?
"a person can vote if and only if they are 18"
if a person can vote, then they are 18
What can you tell me about this statement under the law of detachment?
If an animal is a dog, then it has four legs.
Leonard has four legs.
invalid
Write a q -> r statement to make my conclusion true.
Conclusion: Therefore, if it is Tuesday, I need my pencils.
If I have math class, I need my pencils.
What is the converse of the biconditional
"A number is even if and only if it is a multiple of 2."
If a number is even then it is a multiple of 2.