‌Prime numbers – a number that can

Question 1

What is a prime number?

Answer 1

A number that can only be divided by itself and 1 without remainders. It is not a product of two smaller natural numbers.

Question 2

What is a composite number?

Answer 2

Numbers that have more than two factors and can be formed by multiplying two smaller positive integers.

Question 3

What is a rule of inference?

Answer 3

A logical form or guide consisting of premises (or hypotheses) that draws a conclusion.

Question 4

What is a conjecture?

Answer 4

A mathematical statement which appears to be true, but has not yet been rigorously proved.

Example: The Goldbach Conjecture: Every even integer greater than 2 can be expressed as the sum of two primes.

Question 5

What is an axiom (or postulate)?

Answer 5

A statement that is assumed to be true without proof. A postulate is true based on geometry principles.

Example: In geometry, ‘Through any two points, there is exactly one line.’

Question 6

What is a theorem?

Answer 6

A statement that has been or can be proven to be true based on known facts and mathematical operations.

Example: Pythagorean Theorem a^2 + b^2 = c^2 for a right triangle.

Question 7

What is a lemma (or pre-theorem)?

Answer 7

A minor result whose sole purpose is to help in proving a theorem. It is a stepping stone on the path to proving a theorem.

Question 8

What is a corollary (or post-theorem)?

Answer 8

A result in which the (usually short) proof relies heavily on a given theorem.

Question 9

What is a proof?

Answer 9

A logical argument that shows a mathematical statement is true.

Question 10

What does divisibility mean?

Answer 10

This means a number can be divided without leaving a remainder.

Question 11

What is the greatest common divisor?

Answer 11

The greatest value that can divide two integers evenly.

Question 12

What is the least common multiple?

Answer 12

The smallest positive multiple that two or more numbers share.

Question 13

What are relatively prime integers?

Answer 13

There are no common factors other than 1, meaning no other integer could divide both numbers evenly.

Question 14

What is a direct proof?

Answer 14

A method that involves proving a statement by assuming the hypothesis is true and demonstrating that the conclusion logically follows.

Question 15

What is a proof of contrapositive?

Answer 15

Uses the contrapositive of a conditional statement to prove the statement itself.

Example: p → q is equivalent to ~q → ~p.

Question 16

What is a proof of contradiction?

Answer 16

It is when we assume a proposition is not true and show that it leads to a contradiction, which proves that the proposition is true.

Question 17

What is a proof of exhaustion?

Answer 17

To prove a statement, you must break the statement into a finite amount of cases.

Question 18

What is a proof of counterexamples?

Answer 18

Providing a single example where a statement is false to disprove it.

Example: Disprove ‘All prime numbers are odd.’ Counterexample: 2 is a prime number but is not odd.

Question 19

What is an appeal to authority?

Answer 19

Occurs when we accept a claim merely because someone tells us that an authority figure supports that claim.

Question 20

What is an appeal to force?

Answer 20

Argumentation using force or the threat of force to convince others to accept an argument’s conclusion.

Question 21

What is an appeal to ignorance?

Answer 21

Occurs when you argue that your conclusion must be true, because there is no evidence against it.

Question 22

What is an appeal to pity?

Answer 22

An attempt to persuade others by exploiting and provoking feelings of guilt or pity instead of presenting factual evidence.

Question 23

What is an appeal to people?

Answer 23

Argues that a claim is true simply because that’s what a large number of people believe.

Question 24

What is argumentum ad hominem?

Answer 24

Occurs when, instead of addressing someone’s argument or position, you irrelevantly attack the person or some aspect of the person who is making the argument.

Question 25

What is a circular argument?

Answer 25

A logical fallacy wherein it tries to prove itself using its conclusion as evidence.

Question 26

What is equivocation?

Answer 26

Happens when a word or phrase in an argument has more than one meaning, and the person switches between those meanings to make their point seem more logical or convincing.

Question 27

What is the fallacy of division?

Answer 27

This happens when a person believes that what is true for the entire group or thing also holds true for each of its component pieces.

Question 28

What is a false dilemma?

Answer 28

A logical fallacy that presents only two options or sides to an issue when there are actually more complexities.

Question 29

What is a hasty generalization?

Answer 29

Happens when someone makes a decision or forms a conclusion without having enough evidence or by only looking at one side of the story.

Question 30

What is a red herring?

Answer 30

Occurs when someone introduces an irrelevant point or topic to divert attention from the original issue.

Question 31

What is a slippery slope?

Answer 31

A logical fallacy that assumes a cause-and-effect relationship between events without evidence.

Question 32

What is a strawman fallacy?

Answer 32

The distortion of someone else’s argument to make it easier to attack or refute.