Laws of Syllogism and Detachment

If a student wants to go to university, then the student must study hard and write a good application. Zach wants to go to Caltech.

• Zach must study hard and write a good application.

• No Conclusion can be made.

• Zach will not study but will write a good application.

• Zach got accepted to Caltech.

If two lines do not intersect then they are coplanar and parallel, or skew. Lines AB and CD do not intersect.

• Lines AB and CD are parallel and not coplanar.

• Lines AB and CD are parallel and coplanar or they are skew.

• Lines AB and CD are skew.

• No Conclusion can be made.

Tags

CCSS.8.G.A.1

If there is lightening, then it is not safe to be out in the open. Mary sees lightening from her home.

• It is not safe for the lightening

• No conclusion can be made.

• It is not safe for Marty to be out in the open.

• There is lightening.

Tags

CCSS.HSA.SSE.A.1

If we see John on Monday, then we can ask him over for lunch. We see John on Monday.

• John may eat with us.

• John saw us on Monday

• No conclusion can be made since the hypothesis did not occur.

• We asked John to have lunch with us.

Tags

CCSS.HSS.CP.A.3

If two planes intersect, then their intersection is a line. If two planes are not parallel, then they intersect.

• No Conclusion can be made.

• If two planes intersect they are not parallel.

• If two planes are parallel, then they do not intersect.

• If two planes are not parallel, then their intersection is a iine.

Tags

CCSS.HSG.CO.A.1

If it rains on Tuesday we will not go to the park on Tuesday.

If we do not go to the park on Tuesday we will go on Wednesday.

• If it rains on Tuesday, we will go Wednesday.

• If we go to the park on Wednesday, then it rained on Tuesday.

• No conclusion can be made.

• If we go to the park on Tuesday, then it rained on Tuesday.

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

If you go to the swimming pool, then you will enjoy yourself. If you enjoy yourself, you will want to return.

• If you return to the pool you will enjoy yourself.

• If you enjoy yourself, then you went to the pool.

• If you go to the pool, you will want to return.

• No conclusion can be made.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

If the sun is shining it is a beautiful day. If it is a beautiful day then we will go go hiking.

• If the sun is not shining, we will not go hiking.

• If the sun is shining then we will go hiking.

• No conclusion can be made.

• If we go hiking, then it is a beautiful day.