Bible

Question 1

What is a prime number?

Answer 1

A natural number greater than 1 that has no positive divisors other than 1 and itself

Example: 5 is a prime number because its only divisors are 1 and 5.

Question 2

Is 8 a prime number?

Answer 2

No, because its divisors are more than 1 and 8

Divisors of 8 include 1, 2, 4, and 8.

Question 3

What is a composite number?

Answer 3

A whole number greater than 1 that has more than two positive factors

It can be expressed as a product of smaller whole numbers greater than 1.

Question 4

Give examples of prime numbers.

Answer 4

2, 3, 5, 7

These numbers have exactly two factors: 1 and themselves.

Question 5

What are real numbers?

Answer 5

All numbers that can be represented on a continuous number line, including rational and irrational numbers

Rational numbers include integers and fractions.

Question 6

Define natural numbers.

Answer 6

Counting numbers: 1, 2, 3, …

Natural numbers do not include zero.

Question 7

What are whole numbers?

Answer 7

Natural numbers plus zero: 0, 1, 2, 3, …

Whole numbers include all non-negative integers.

Question 8

What are integers?

Answer 8

Whole numbers and their negative counterparts: …, -3, -2, -1, 0, 1, 2, 3, …

Integers include all positive and negative whole numbers.

Question 9

Define rational numbers.

Answer 9

Numbers that can be expressed as a fraction of two integers (e.g., 1/2, -3/4, 0.75)

Rational numbers include both positive and negative values.

Question 10

What is a perfect square?

Answer 10

A number that can be expressed as the product of an integer with itself

Example: 9 is a perfect square because it is equal to 3^2.

Question 11

What is an integer multiple?

Answer 11

A product of a number and any integer

Example: 12 is a multiple of 3 because 12 = 3×4.

Question 12

What does M(x) mean in the context given?

Answer 12

x is an integer multiple of 4

This means 4 is multiplied by some integer (n) to get x.

Question 13

If x=8, what is the integer n when x is an integer multiple of 4?

Answer 13

n is 2

Because 8 = 4×2.

Question 14

What are consecutive numbers?

Answer 14

Integers that follow one another in order, such that if a is an integer, then b=a+1

Example: If a is 3, then b is 4.

Question 15

Fill in the blank: A perfect square is a number that can be expressed as the product of an integer with _______.

Answer 15

itself

Question 16

What is the definition of an even integer?

Answer 16

An integer x is even if there is an integer k such that x=2⁢k.

Question 17

What is the definition of an odd integer?

Answer 17

An integer x is odd if there is an integer k such that x=2⁢k+1.

Question 18

What does the parity of a number refer to?

Answer 18

The parity of a number is whether the number is odd or even.

Question 19

If two numbers are both even or both odd, what can be said about their parity?

Answer 19

Then the two numbers have the same parity.

Question 20

What can be said about the parity of one odd and one even number?

Answer 20

Then the two numbers have opposite parity.

Question 21

What is the technique used to determine if a number is even or odd?

Answer 21

The technique relies on the fact that any even number, when divided by 2, will result in an integer with no remainder.

Question 22

What does it mean if you can factor out a 2 completely?

Answer 22

It’s even.

Question 23

What does it mean if you can factor out a 2, leaving a remainder of 1?

Answer 23

It’s odd.

Question 24

How can you show that 0.677 is a rational number?

Answer 24

By giving an integer x such that r=x/y, where x=677 and y=1000.

y correlates to the decimal place.

Question 25

Is 0 a rational number?

Answer 25

Yes, zero is a rational number because it can be expressed as a ratio of two integers, such as 0/1 or 0/2. A rational number is any number that can be written as a fraction a/b, where a and b are integers, and b is not zero.

Question 26

What is the definition of a rational number?

Answer 26

A number r is rational if there exist integers x and y such that y≠0 and r=x/y.

Question 27

How is it denoted that an integer x divides an integer y?

Answer 27

The fact that x divides y is denoted x∣y.

Question 28

What does it mean if x does not divide y?

Answer 28

This is denoted x∤y.

Question 29

What is a prime number?

Answer 29

A prime number is a natural number greater than 1 that *has no positive divisors* other than 1 and itself.

Question 30

What is a composite number?

Answer 30

A composite number is a whole number greater than 1 that has more than two positive factors.

Question 31

What are real numbers?

Answer 31

Real numbers are all numbers that can be represented on a continuous number line, including rational and irrational numbers.

Question 32

What is a perfect square?

Answer 32

A perfect square is a number that can be expressed as the product of an integer with itself.

Question 33

What is an integer multiple of a number?

Answer 33

An integer multiple of a number is a product of that number and any integer.

Question 34

Define consecutive integers.

Answer 34

If a is an integer, then b=a+1.

Question 35

True or False: 2 is a prime number.

Answer 35

True.

Question 36

True or False: A real number x is negative if and only if x < 0.

Answer 36

True.

Question 37

True or False: 1 is a prime number.

Answer 37

False.

Question 38

What can be said about 0?

Answer 38

* Its associated in every group besides irrational numbers. * The number 0 is neither positive nor negative.

Question 39

What is the definition of superscript & subscript?

Answer 39

Question 40

# the symmetric difference operation X⊕Y=(X∪Y)−(X∩Y), In other words?

Answer 40

X⊕Y=(X−Y)∪(Y−X)

Question 41

# the symmetric difference operation A⊕A ## Footnote X⊕Y=(X−Y)∪(Y−X)

Answer 41

## Footnote X⊕Y=(X∪Y)−(X∩Y)

Question 42

# the symmetric difference operation A⊕A ## Footnote X⊕Y=(X−Y)∪(Y−X)

Answer 42

## Footnote X⊕Y=(X∪Y)−(X∩Y)

Question 43

# the symmetric difference operation A⊕(A⊕B) ## Footnote X⊕Y=(X−Y)∪(Y−X)

Answer 43

## Footnote X⊕Y=(X∪Y)−(X∩Y)

Question 44

# Cartesian Product What is the method to write two sets `X * Y` in roster notation?

Answer 44

To write the final answer in roster notation, you enclose all the ordered pairs you found within curly brackets and separate them with commas.

Question 45

# Cartesian Product The notation `X^4` is shorthand for what?

Answer 45

The notation `X^4` is a shorthand for the Cartesian product of set X with itself four times: `X×X×X×X`. ## Footnote It shows each position can be any element from the set