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Law of Detachment
Law of Syllogism
Detachment or Syllogism
Symbolic Notation
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

If you live in Dallas, then you live in Texas. Levi lives in Dallas.

Levi lives in Texas.

100

A conditional statement symbolic notation.

What is p > q

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. Mount McKinley is the highest mountain in Alaska. 

Alaska's Mount McKinley is the highest in the USA.

200

The symbolic Notation is represented by ~p > ~q 

What is Inverse

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 school, then you will get good grades.

If you like English Class, then you get good grades.

300

If you smile, then you are happy. If you are happy, then you are nice.

If you smile, then you are nice.

300

The symbolic Notation is represented by ~q > ~p

What is Contra Positive?

400

If n is prime and greater than two, then n squared is an odd number.  9 squared is an odd number.

No valid conclusion

400

If my dad does not pay my brother's college tuition, then my brother may not graduate from College. If my brother does not graduate college , then my brother will be a salesman.

If my dad does not pay my brothers tuition, then my brother will be a salesman

400

If n is prime, then 2n is even. If 2n is even, then 2n-1 is odd.

If n is prime, then 2n-1 is odd.

400

The symbolic Notation is represented by q > p

What is Converse?

500

If an angle is obtuse, then it is not acute. Angle m is 91.9 degrees.

It is not acute

500

If you go to Grand Valley State University, then you are a Laker. If you are a Laker, then you know the 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.

If you ate breakfast, then you will do better on your test.

500

This law has a symbolic notation of  

p > q, then q > r, and p > r.


What is Syllogism?