Law of Detachment
If it snows, then school will be cancelled.
School was cancelled.
What is Inconclusive?
If you live in Redlands, then you live in California. If you live in California, then you live in the USA.
What is "lf you live in Redlands, then you live in the USA?"
If you live in Dallas, then you live in Texas. If you live in Texas, then you live in the 28th state to enter the union.
Luke lives in Dallas.
What is "Luke lives in the 28th state to enter the union?"
p <---> q
What is a biconditional - "if and only if"
Hypothesis of "If I am thirsty, then I drink water."
What is "I am thirsty?"
If a droid's main function is protocol, then the droid speaks many languages.
C-3P0 is a protocol droid.
What is "C-3P0 speaks many languages"?
If 3x-5 = 37 then x = 14. If x = 14, then x2 - 8 = 188.
What is "If 3x-5 = 37, then x2 - 8 = 188"?
Alaska's Mount McKinley is 20,320 feet.
If an Alaskan mountain is over 20,300 feet, then it is the highest in Alaska. If a mountain is the the highest in Alaska, then it is the highest in the USA.
What is "Mount McKinley is the tallest mountain in the USA?"
p ---> q
q ---> r
p ---> r
What is the Law of Syllogism?
Conclusion of "If I am rich, then I buy Mrs. Nice gifts."
What is "I buy Mrs. Nice gifts?"
If two lines are parallel, then they do not intersect. Line m is parallel to line n.
Line m and n do not intersect.
If a value is even, then it is divisible by 2. If a value is divisible by 2, then it ends in 0, 2, 4, 6, or 8.
What is "If a value is even, then it ends in 0, 2, 4, 6, or 8?"
If you smile, then you are happy. If you are happy, then you are nice.
Ethan is nice.
What is "Inconclusive?"
If an animal is hungry, then it hunts for food.
- The lion is hungry.
What is the Law of Detachment?
Logical Conclusion: The lion hunts for food.
"If the Steelers lose, then Mrs. Nice will be sad"
q V p
What is "The Steelers lose or Mrs. Nice will be sad?"
If n is prime and greater than two, then n squared is an odd number.
n = 9
What is Inconclusive? 9 does not fit the hypothesis criteria of being prime.
If 7x - 12 = 23 , then x = 5. If x = 5, then x/100 = 0.05.
What is "If 7x - 12 = 23, then x/100 = 0.05?"
If n is prime, then 2n is even. If 2n is even, then 2n-1 is odd.
7 is prime.
What is "14 - 1 is odd?"
If you are in Mrs. Nice's class, then you are learning Geometry. If you are learning Geometry, then you are happy.
Law of Syllogism
If you are in Mrs. Nice's class, then you are happy.
"If the Steelers lose, then Mrs. Nice will be sad"
q <--> p
What is "The Steelers lose and Mrs. Nice will be sad?"
If an angle is obtuse, then it is not acute.
Angle m is 89.9 degrees.
What is Inconclusive?
Angle m is not obtuse - does not fit hypothesis.
If you go to ACA, then you are an eagle. If you are an eagle, then you can fly.
What is "If you go to ACA, then you can fly?"
If you ate lunch, then you won't be hungry in 6th or 7th period. If you aren't hungry in 6th or 7th period, then you will focus better.
Carl had a big dinner yesterday and eggs for breakfast.
What is "Inconclusive?"
If an animal is hungry, then it will hunt for food.
- A bear hunts for food.
What is Law of Detachment?
What is Inconclusive?
If the Steelers lose, then Mrs. Nice will be sad
The Steelers lose and Mrs. Nice is not sad.
p ^ ~ q