2.1-2.2 Geometry

In your own words, what is inductive reasoning?

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What is deductive reasoning?

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Identify the type of reasoning used in the following argument: "The sun has risen in the east every day in recorded history. Therefore, the sun will rise in the east tomorrow."

• Deductive reasoning

• Inductive reasoning

• Abductive reasoning

• Analogical reasoning

Answer explanation

The argument is based on past observations to predict a future event, making it an example of inductive reasoning.

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DOK Level 2: Skill/Concept

Determine whether the following argument is deductive or inductive: "If it rains, the ground will be wet. It is raining. Therefore, the ground is wet."

• Deductive

• Inductive

• Abductive

• Analogical

Answer explanation

The argument follows a deductive reasoning pattern where the conclusion necessarily follows from the premises, making it a deductive argument.

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DOK Level 2: Skill/Concept

Organize these options into the right categories

Groups:

(a) Inductive Reasoning

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(b) Deductive Reasoning

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(c) BAD Reasoning

• After observing that the last five times it rained, I got wet, I conclude that I will get wet the next time it rains.

• I heard that eating chocolate is unhealthy, so I will never eat anything sweet again.

• My brother is bad at math, so all boys must be bad at math.

• The sun has risen in the east every day of my life, so it will rise in the east tomorrow.

• My neighbor's cat is friendly, so all cats must be friendly.

• Every time I eat peanuts, I feel sick, so I must be allergic to peanuts.

• If a shape is a square, then it has four equal sides. This shape is a square, therefore it has four equal sides.

• Uses observations

• If it rains, the ground will be wet. It is raining, therefore the ground is wet.

• All mammals have a backbone. A dolphin is a mammal, therefore a dolphin has a backbone.

• Samantha has a dog and it has four legs, therefore all dogs have four legs.

• If I study hard, I will pass the exam. I studied hard, therefore I will pass the exam.

• My friend said that all birds can fly, and since penguins are birds, they can fly too.

• Everyone I know who has a cat is happy, so having a cat must make you happy.

• Since I have seen many swans and they are all white, I conclude that all swans are white.

• I failed my last exam, so I will fail all my future exams.

• Since I saw a black cat today, I will have bad luck for the rest of the week.

A _________ is an unproven statement that is based on observations.

• theory
• fact
• conclusion
• hypothesis

_________ uses facts, definitions, accepted properties, and the laws of logic to form a logical argument

• Deductive reasoning
• Inductive reasoning
• Abductive reasoning
• Intuitive reasoning

You use _________ when you find a pattern in specific cases and then write a conjecture for the general case.

• analytical reasoning
• abductive reasoning
• inductive reasoning
• deductive reasoning

A _________ is a specific case for which the conjecture is false.

• counterexample
• theorem
• hypothesis
• example

A conditional statement, symbolized by p → q, can be written as an “if-then” statement in which p is the ___________.

• consequent
• antecedent
• premise
• hypothesis