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Inductive and Deductive Reasoning
Conditional and Biconditional Statements
Proofs
Bonus
Laws of Syllogism and Detachment
100

What are inductive and deductive reasoning?

Inductive reasoning is the process of reasoning that a statement is true because specific cases are true. Deductive reasoning is the process of reasoning that a statement is true by logic or fact.

100

Identify the hypothesis and conclusion of the conditional statement. If I answer a phone call, then I have a phone.

The hypothesis is if I answer a phone call. The conclusion is then I have a phone.

100
Write a two column proof. Given: Q is the midpoint of PR and PQ=ST Prove: QR=ST
Q is the midpoint of PR (given) QR=PQ (definition of midpoint) PQ=ST (given) QR=ST (transitive property of =)
100

The team the blazers beat in the western conference semis last season

Who is the Denver Nuggets

100

Determine if the conjecture is valid by the Law of Detachment. Given: If Sue buys a TV, then Sue must have money. Sue has money. Conjecture: Sue bought a TV.

Invalid.

200
There's a myth that a duck's quack does not echo. So, a group of scientists observed a duck in a special room and discovered that its quack did echo proving the myth false. Did the scientists use deductive or inductive reasoning?
Inductive reasoning.
200
Write a conditional statement from the following fact. A dog has fur.
If it is a dog, then it has fur.
200
Write a two column proof. Given:FH=GI, FH=2x+4, and GI=5x-2 Prove:x=2
FH=GI, FH=2x+4, and GI=5x-2 (given) 2x+4=5x-2 (substitution property) 2x+6=5x (Addition property of =) 6=3x (subtraction property of =) 2=x (division property of =) x=2 (symmetric property of =)
200
The current Blazer who played for the Heat last season

Hassan Whiteside

200

Determine if the conjecture is valid by the Law of Syllogism. Given: If you are in Lansing, then you are in Michigan. If you are in Michigan, then you are in the USA. Conjecture: If you are in Lansing, then you are in the USA.

Valid

300
Determine whether the following statements are an example of deductive or inductive reasoning. Dogs have fur, and Fido is a dog. Therefore, Fido has fur.
Deductive reasoning
300
Write the defenition as a biconditional. An acute angle is an angle whose measure is less than 90 degrees.
It is an acute angle iff its measure is less than 90 degrees.
300
Write a two column proof. Given: AB=BC, DF=FG,and AB=DF Prove:AC=DG
AB=BC, DF=FG,and AB=DF (given) BC=DF=FG (substitution property) AB+BC=AC and DF+FG=DG (segment addition postulate) AB+BC=DG (substitution property) AC=DG (substitution property)
300

This famous Chicago Bull also played for the Blazers

Who is Scottie Pippen

300

Determine whether the conjecture is valid by the Law of Detachment. Given: If Nancy makes dinner, then Nancy must have food. Nancy makes dinner. Conjecture: Nancy has food.

Valid.

400
There is a legend that if you eat carrots it improves your night vision. A group of scientists observed if a person who had eaten a lot of carrots could see well at night. Is this an example of inductive or deductive reasoning?
Inductive reasoning
400
Define inverse, converse, contrapositive, negation, and truth value.
The inverse is the statement formed by negating the hypothesis and conclusion. The converse is the statement formed by exchanging the hypothesis and conclusion. The contrapositive is the statement formed by negating and exchanging the hypothesis and conclusion. Negation is the contradiction of a statement using "not." The truth value of a statement is either true (T) or false (F).
400

The name of the arena the Blazers play in before it was called the Moda Center

What is the Rose Garden

400
What property justifies subtracting the same amount from both sides of an equation?
The subtraction property of =.
400
Determine whether the conjecture is valid by the Law of Syllogysm. Given: If it is a square, then it is a rectangle. If it is a rectangle, then it is a polygon. Conjecture: If it is a polygon, then it is a square.
Invalid
500
There is a myth that walking under a ladder is bad luck. A group of scientists observed a person who had stepped under a ladder. They found the person had good luck since he won the lottery and concluded the myth was false. Why is this an example of inductive reasoning?
It is inductive reasoning beacause it is based on observations.
500
Write the converse, inverse, contrapositive, and truth value for the following conditional statement. If it is a cat, then it has a tail.
The inverse is if it is not a cat, then it has no tail (F). The converse is if it has a tail, then it is a cat (F). The contrapositive is if it has no tail, then it is not a cat (T).
500

The country Arvydas Sabonis was from

What is Lithuanian?

500
What two properties would you need to know to prove the following statement with the given information? Given: SR=TU, TU=2x, and SR=6 Prove: x=3
Substitution property and division property of =.
500
Determine whether the conjecture was reached using the Law of Syllogism or Detachment. Given: If it is a square, then it is a diamond. ADFG is a square. Conjecture: ADFG is a diamond.
Law of Detachment