Finite Mathematics - C277

pΛq

True if both are true, else false

p->q

if p then q

Symbolic Form V

OR

Symbolic Form Λ

AND

Symbolic Form ~

"it is not the case that"

=> or "right arrow"

If...Then...

↔

"implies and is implied by" or "....if and only if..."

pVq

if p or q are true then "true", else if both are false then "false"

Prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

prime factorization

Breaking down a composite number until all of the factors are prime.

prime factorization process

divide number by smallest prime number that it evenly divides into, then repeat until you have the list of prime numbers that make the big number.

Truncate

Similar to rounding but never round up. In other words drop to the place indicated.

Double sided arrow

if and only if, or the if statement can be reversed and still be true.

parentheses

group statements ~(pVq) you negative both statements. Often express in statements as a comma(,).

Conjunction

and, Λ, both statements must be true for the whole thing to be true.

Disjunction

or, V, only false when both statements are false.

Negation

~, not, the opposite of the statement.

Conditional statement

arrow, if...then, only false when if statement is true and then statement is false.

Bi-Conditional statement

double arrow, if and only if...then, only true if both components have the same truth value.

Truth Table order

TT, TF, FT, FF

Truth Table Steps

Simple statements, Negations of simple if needed, complex statements, answer

Commutative Property

The property that says that two or more numbers can be added or multiplied in any order without changing the result. example:a+ b= b + a.

Associative Property

Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication(a × b) × c = a × (b × c)

Distributive Property

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac

Closure Property

A set is closed under an operation if and only if the operation on two elements of the set produces another element of the set. If an element outside the set is produced, then the operation is not closed. Example: 3 + 5 = 8.
Not close: 3÷2=1.5(1.5 is not an integer).

power rule of exponents multiplication

when multiplying exponents together, just add the exponents x^m * x^n = x^(m+n)

Integer

whole numbers that include positive numbers, negative numbers, and zero. They extend infinitely in both directions: …,−3,−2,−1,0,1,2,3,……,−3,−2,−1,0,1,2,3,…

Natural numbers

the counting numbers starting from 1 and extending infinitely:1, 2, 3, ......

Rational Numbers

Any number that can be expressed as a fraction of two integers. example: ½, ¼ ,

Irrational Numbers

Any real number which cant be expressed as a fraction of two integers. examples pie or square root of 2, π ,e.

Real Numbers

all numbers that can be represented on a number line. encompassing both rational and irrational numbers

Whole Numbers

a set of numbers that include all the non-negative integers. They are used for counting and ordering, and they do not include fractions, decimals, or negative numbers. ex. 0,1,2,3,4,5,…

A family goes on a road trip totaling 1885 miles.

If after 4 hours they have traveled 260 miles, how many hours more will it take to reach the destination (assuming the same rate of speed for the remainder of the trip)?

25 hours

2(–3)² – 4(–5)²

Simplify the above expression by applying the order of operations.

–82

2[18 – 6(3² – 5) / 8 + 4]

Simplify the above expression.

38

√225/3

5√3

The ratio of women to men at a certain college is 5 to 4. There are 2,480 men.

What is the total population of the college?

5580

Some dogs are friendly

At least one dog is friendly

all dogs are friendly

there are no dogs that are not friendly

some dogs are not friendly

not all dogs are friendly

no dogs are friendly

all dogs are not friendly