Deductive Reasoning

Used to prove that a conjecture is false.

• Counterexample
• Inductive Reasoning
• Concluding statement
• Conjecture

A type of reasoning that uses general facts, definitions, and accepted properties in a logical order to write a logical argument.

• Inductive

• Deductive

• Logic

• Reasoning

An unproven statement which is based on observations.

• Reasoning

• Conclusion

• Conjecture

• Logic

Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.

• Inductive

• Deductive

All bears are mammals, all mammals have kidneys; therefore all bears have kidneys. 

• Deductive
• Inductive

Obtuse angles are greater than 90 degrees.  This angle is 110 degrees, so it is obtuse. 

• Deductive
• Inductive

If I will not study, I will fail the exam.

If I will fail the exam, I will be scolded by my parent.

Therefore, if I will not study, I will be scolded by my parent.

What law is being used in this argument?

• Law of Detachment

• Law of Contrapositive

• Law of Syllogism

• Law of Converse

p→q q→r ∴p→r Which law is modeled? #32

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Use the Law of Syllogism to make a conclusion.  If a number is divisible by 10, then it is divisible by 2.  If a number is divisible by 2, then it is even. #38

• If a number is divisible by 10, then it is even,
• If a number is even, then it is divisible by 10.
• If a number is divisible by 2, then it is even.
• If a number is even, then it is divisible by 2.

Use the Law of Syllogism to make a conclusion. If the perimeter of a square is 20 ft, then the length of a side is 5 ft. If the length of a side of a square is 5 ft, then the area is 25 ft². #39

• If the side of a square is 5 ft, then the perimeter is 20 ft.
• If the perimeter of a square is 20 ft, then the area is 25 ft²
• If the area of a square is 25 ft², then the side length is 5 ft. 
• If the are of a square is 25 ft², then the perimeter is 20 ft.