GEMath 1 PRELIMS
a. have lids b. a lid L c. L is a lid for P
Fill in the blanks: a. All pots ________ b. For all pots P, there is ___________. c. For all pots P, there is a lid L such that ___________.
Universal existential statement
For all real numbers r, there is a real number s such that s is an additive inverse for r.
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Given: A = {1, 5, 9}, B = {2, 4, 6,} and C = {0, 2, 4, 6, 8} Write the universal set for all three sets A, B, and C.
Mathematics
It helps organize patterns and regularities in the world. It also helps predict the behavior of nature and phenomena in the world, as well as, help human exert control over occurrences in the world for the advancement of our civilization.
Patterns
It indicates a sense of structure and organization that it seems only humans are capable of producing these intricate, creative, and amazing formations.
Symmetry
It indicates that you can draw imaginary line across an object and the resulting parts are mirror images of each other.
Universal Existential Statement
It is a statement that is universal because its first part says that I've certain property is true for all objects of a given time, and it is existential because its second part asserts the existence of something.
Fibonacci sequence
It is formed by adding the preceding two numbers, beginning with 0 and 1.
Axiom of Extension
It says that a set is completely determined by what its elements are—not the order in which they might be listed or the fact that some elements might be listed more than once.
True
"For all polygons P, if P is a triangle, then P has three sides." The sentence above is an example of Universal Conditional Statement. (T or F)
Conditional statement
"If b is an eagle, then b is a bird." Which statement best suits on the sentence above?
Pattern
A _______ is a regular, repeated, or recurring forms or design.
Universal existential statement
A __________________ is a statement that is universal because its first part says that a certain property is true for all objects of a given type.
Universal Statement
A statement that says a certain property is true for all elements in a set. Ex. All positive numbers are greater than zero.
True
An existential universal statement is a statement that is existential because its first part asserts that a certain object exists and is universal because its second part says that the object satisfies a certain property for all things of a certain kind. (T or F)
bilateral symmetry
Body plan in which only a single, imaginary line can divide the body into two equal halves. or the left and right portions are exactly the same.
H Explanation: Convert each letter to its numerical equivalent in the alphabet e.g. the letter "C" is assigned the number "3". Afterwards, for each row, multiply the numerical equivalents of the first two columns in order to calculate the letter int he third column.
Challenge question: What is the missing letter? E C O B A B G B N D B ?
U and V
Let A={2,4} and B={1,3,5} and define relation U, V, and W from A to B as follows: For all (x,y)∈A×B, (x,y)∈U means that y−x>2 (x,y)∈V means that y−1=x2 W={(2,5),(4,1),(2,3)} Which of relation is a function?
R = {(5,5), (6,5), (6,6)}
Let A={4,5,6} and B={5,6,7} and define relation R as follows: For all (x,y)∈A×B, (x,y)∈R means that x≥y. Which ordered pairs are in R? • R = {(4,5), (4,6), (5,6), (4,7), (5,7), (6,7)} • R = {(5,5), (6,)} • R = {(4,5), (6,5), (4,6), (5,6), (4,7), (5,7), (6,7)} • R = {(5,5), (6,5), (6,6)}
D = {G, O, A, T}
Let D = {G, O, A, T}. Which of the following is not a proper subset? D = {G, O, A, T} D = {G, O, T} D = {O} D = { }
True
Mathematics is always around us. (T or F)
True
Nonnegative integers are also called as Natural numbers. (T or F)
Exponential Growth Model
Population growth and bacterial decay can be modeled by the exponential growth or decay formula A=Pe^rt.
discrete
Since every integer is a real number, and because the integers are all separated from each other, the set of integers is called __________.
377
Starting with the first Fibonacci number, Fib(1) = 0, Fib(2) = 1, Fib(3) = 1, Fib(4) = 2. what is the 15th Fibonacci number Fib(15)?
Z^+
Symbol for positive integers
R^+
Symbol for positive real numbers
rotational symmetry
The ability of a figure to be rotated less than a full circle and exactly match its original image. Or it is rotating a figure by several degrees, and still achieve the same appearance as the original position.
Golden Ratio
The ratios of two Fibonacci numbers approximate the ________________, which is considered as the most aesthetically pleasing proportion.
continuous
The real number line is called ________ because it is imagined to have no holes.
True
The unrestricted use of set-builder notation can lead to genuine contradictions in set theory.
Set
The use of this word as a formal mathematical term was introduced in 1879 by George Cantor.
Existential statement
This is a type of statement which says that there is at least one thing for which the property is true. What is this?
Cartesian Plane
This term is often used to refer to a plane with a coordinate system.
21
What comes next in the sequence? 0, 1, 1, 2, 3, 5, 8, 13, __
IVJ
What completes the following pattern? CSD, ETF, GUH, ___, KWL
Z
What is the symbol for "set of all integers"
Q
What is the symbol for "set of all rational numbers, or quotients of integers"
R
What is the symbol for "set of all real numbers"
Conditional statement
What kind of a statement says that if one thing is true then some other thing also has to be true?
Universal Conditional Statement
What kind of statement is this? All dogs are mammals.
Universal existential statement
What kind of statement is this? Every real number has an additive inverse.
Universal Conditional Statement
What kind of statement is this? For all dogs a, a is a mammal.
Universal existential statement
What kind of statement is this? For all real numbers r, there is an additive inverse for r.
Universal Conditional Statement
What kind of statement is this? If a is a dog, then a is a mammal.
Universal Conditional Statement
What kind of statement is this? If an animal is a dog, then the animal is mammal.
216
What number comes next in 1, 8, 27, 64, 125, __?
Existential universal statement
What statement is this? There is a positive integer m such that every positive integer is greater than or equal to m.
Existential Universal statement
What statement is this? There is a positive integer m that is less than or equal to everybody did integer.
Existential universal statement
What statement is this? There is a positive integer m with the property that for all positive integers n, m is less than or equal to n.
Existential universal statement
What statement is this? There is a positive integer that is less than or equal to every positive integer
The set of odd natural numbers divisible by 2.
Which of the following is an empty set? • The set of even integers divisible by 3. • The set of odd natural numbers divisible by 2. • The set of prime numbers divisible by 2. • The set of prime numbers between 25 and 30.
C only - {H}∈{{I},{N},{H},{S}}
Which of the following is/are a true statement? A. {P}∈{C,P,U} B. S⊆{W,E,S,T} C. {H}∈{{I},{N},{H},{S}} D. {T}⊆{{W},{I},{T}}
M = {..., -10, -9, -8, -7, -6, -5 }
Write the elements of the following set M={x:x∈Z−,x≤−5}
A = {x : x is a positive multiple of 3 greater than 10}
Write the following set in a set builder form. A = {12, 15, 18, 21, 24,...}
Existential statement
________________ is a type of statement which says that at least one thing for which is true.
Golden Rectangle
a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle, which can be repeated infinitely inside each section.
Conditional Statement
a statement that can be written in if-then form; it says that if one things is true then some other thing also has to be true. Ex. If 378 is divisible by 18, then 378 is divisible by 6.
Existential universal statement
a statement that is existential because its first part asserts that a certain object exists and is universal because its second part says that the object satisfies a certain property for all things of a certain kind
Existential Statement
a statement that says that there is at least one thing for which the property is true. Ex. There is a prime number that is even. (This prime even number is "2")
a. person in my class; every person in my class b. at least as old as every person in my class c. at least as old as q
a. Some ______ is at least as old as ______ b. There is a person p in my class such that p is ____________ c. There is a person p in my class with the property that for every person q in my class, p is ________
Universal Conditional Statement
is a statement that is both universal and conditional. ex. For all animals a, if a is a dog, them a is a mammal.
Variable
is sometimes though of as a mathematical "John Doe" because you can use it as a place holder when you want to talk about something you (1) you imagine that has one or more values but don't know what they are, or (2) you want whatever you say about it to be equally true for all elements in a given set.
Golden Ratio
it can be expressed as the ratio between two numbers, if the latter is also the ratio between the sum and the larger of the two numbers.
Sequence
it is an ordered list of numbers, called "terms" that may have repeated values. The arrangement of these terms is set by a definite rule. Its terms could be generated by applying the rule to previous terms of the sequence.
N
symbol for natural numbers
Z^-
symbol for negative integers
Z^nonneg
symbol for nonnegative integers: 0, 1, 2, 3, 4, 5, ...
Discrete Mathematics
this comes from the distinction between continuous and discrete mathematical objects.
