Law of Detachment
Law of Syllogism
Detachment and Syllogism
100
If a student gets an A on a final exam, then the student will pass the course. Amy got an A on her Music Exam.
Amy passed Music.
100
If you live in Grand Rapids, then you live in Michigan. If you live in Michigan, then you live in the USA.
lf you live in Grand Rapids, then you live in the USA.
100
What can you conclude? If you live in Dallas, then you live in Texas. Levi lives in Dallas. If you live in Texas, then you live in the 28th state to enter the union.
Levi lives in Texas. If you live in Dallas, then you live in the 28th state to enter the union.
200
If a student wants to go to college, then the student must study hard. Ryan wants to go to CMU.
Ryan must study hard.
200
If you like tomatoes, then you like salsa. If you like salsa, then you like tacos.
If you like tomatoes, then you like tacos.
200
Alaska's Mount McKinley is 20,320 feet. If a mountain is the the highest in Alaska, then it is the highest in the USA. If an Alaskan mountain is over 20,300 feet, then it is the highest in Alaska.
If an Alaskan mountain is over 20,300 feet, then it is the highest in the USA. Alaska's Mount McKinley is the highest in the USA.
300
If two lines are parallel, then they do not intersect. Line m is parallel to line n.
Line m and n do not intersect.
300
If you like English class, then you like school. If you like reading, then you like English class.
If you like reading, then you like school.
300
If you smile, then you are happy. If you are happy, then you are nice. Joe smiles.
Joe is nice. If you smile, then you are nice.
400
If n is prime and greater than two, then n squared is an odd number. 9. So, 9 squared is an odd number.
Not possible. 9 does not fit the hypothesis criteria of being prime.
400
If my dad does not pay my brother's college tuition, then my brother may not graduate from CMU. If my brother climbs one more mountain without his helmet, then my dad will not pay his college tuition.
If my brother does not wear his helmet when he climbs, then he will not graduate from CMU.
400
If n is prime, then 2n is even. If 2n is even, then 2n-1 is odd. 7 is prime.
If n is prime, then 2n-1 is odd. 2(7)-1=14-1=13, ok!
500
If an angle is obtuse, then it is not acute. Angle m is 89.9 degrees.
Not possible to conclude anything. Angle m is not obtuse - does not fit hypothesis.
500
If you go to Grand Valley State University, then you are a Laker. If you are a Laker, then you know GVSU's mascot is a sailor.
If you go to GVSU, then you know the mascot is a sailor.
500
If you ate breakfast, then you won't be hungry in 1st hour. If you aren't hungry in 1st hour, then you will do better on your test. Carl had a big dinner the night before and only had orange juice before 1st hour.
If you ate breakfast, then you will do better on your test. No conclusion about Carl.
M
e
n
u