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Logic

Deductive vs Inductive Reasoning

Lesson

Reasoning comes in two big flavors. Knowing which one you’re doing matters because they offer different levels of certainty.

Deductive reasoning

From general rules to a specific conclusion. If the rules and premises are true, the conclusion must be true.

Example: “All squares have 4 sides. This is a square. So this has 4 sides.”

Inductive reasoning

From specific observations to a general pattern. The conclusion is likely but not guaranteed.

Example: “The sun rose every day this year. So it will rise tomorrow.”

How to type your answer

1 = deductive, 2 = inductive.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

“All squares have 4 sides. This is a square. So it has 4 sides.”\text{``All squares have 4 sides. This is a square. So it has 4 sides.''}

Problem 2

“Sun rose every day this year. So it will rise tomorrow.”\text{``Sun rose every day this year. So it will rise tomorrow.''}

Problem 3

“If even, div by 2. 8 is even. So 8 div by 2.”\text{``If even, div by 2. 8 is even. So 8 div by 2.''}

Problem 4

“I’ve seen 5 swans, all white. So all swans are white.”\text{``I've seen 5 swans, all white. So all swans are white.''}

Practice

Standard problems matching the lesson.

Problem 5

“All mammals are warm-blooded. A dog is mammal. So dog is warm-blooded.”\text{``All mammals are warm-blooded. A dog is mammal. So dog is warm-blooded.''}

Problem 6

“Every test I took had multiple choice. So all tests are multiple choice.”\text{``Every test I took had multiple choice. So all tests are multiple choice.''}

Problem 7

“All primes > 2 are odd. 7 is prime > 2. So 7 is odd.”\text{``All primes > 2 are odd. 7 is prime > 2. So 7 is odd.''}

Problem 8

“The first 100 even numbers are divisible by 2. So every even number is.”\text{``The first 100 even numbers are divisible by 2. So every even number is.''}

Problem 9

“If a triangle’s angles sum to 180°, then this one does too.”\text{``If a triangle's angles sum to 180°, then this one does too.''}

Problem 10

“Every car I see is red today. So all cars today are red.”\text{``Every car I see is red today. So all cars today are red.''}

Problem 11

Geometry proof using axioms and theorems\text{Geometry proof using axioms and theorems}

Problem 12

Scientist observing 100 trials and forming a hypothesis\text{Scientist observing 100 trials and forming a hypothesis}

Problem 13

“All right angles measure 90°. This is a right angle. So it’s 90°.”\text{``All right angles measure 90°. This is a right angle. So it's 90°.''}

Problem 14

“It rained on Monday, Tuesday, Wednesday. So it’ll rain Thursday.”\text{``It rained on Monday, Tuesday, Wednesday. So it'll rain Thursday.''}

Problem 15

Mathematical induction proof\text{Mathematical induction proof}

Problem 16

“5 students from each grade studied. So most students study.”\text{``5 students from each grade studied. So most students study.''}

Problem 17

“Triangles all have 3 sides. ABC is a triangle. So ABC has 3 sides.”\text{``Triangles all have 3 sides. ABC is a triangle. So ABC has 3 sides.''}

Problem 18

“Pencils I’ve checked are HB. So all pencils are HB.”\text{``Pencils I've checked are HB. So all pencils are HB.''}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Modus ponens reasoning\text{Modus ponens reasoning}

Problem 20

Generalizing from a sample\text{Generalizing from a sample}

Problem 21

“All ravens I’ve seen are black. So all ravens are black.”\text{``All ravens I've seen are black. So all ravens are black.''}

Problem 22

“If x>5 then x>0. x=7. So x>0.′′\text{``If } x > 5 \text{ then } x > 0. \ x = 7. \text{ So } x > 0.''

Problem 23

Predicting future based on past data\text{Predicting future based on past data}

Problem 24

Proof by contradiction\text{Proof by contradiction}

Problem 25

Forming a scientific hypothesis from experiment results\text{Forming a scientific hypothesis from experiment results}

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