MATH 302 Week 2 Exam NEWEST 2025 COMPLETE
QUESTIONS AND CORRECT DETAILED ANSWERS
(VERIFIED ANSWERS) |ALREADY GRADED A+||BRAND
NEW VERSION!!
Suppose a UT alum tells you their license plate is H00K3M. If you had a listing of all the
registered vehicles in the United States, would you be able to identify the vehicle belonging to
that person? Explain why or why not, using the idea of a one-to-one correspondence. -
CORRECT ANSWER- You would be able to identify the vehicle because there is a one-to-one
correspondence between licence plates and cars.
A professor wishes to distribute one exam paper to each student in the class. What is the more
efficient method: count students, or pass out exams? How does this relate to one-to-one
correspondence? - CORRECT ANSWER- The most efficient method is to pass out exams. Each
student present will receive one exam. This is the one-to-one crrespondence
Are there an infinite number of grains of sand on the Earth? Explain. - CORRECT ANSWER-
There is a finite number of grains of sand on Earth. It would be tedious but one could count or
estimate the number of grains of sand.
Define the term cardinality. When do two sets have the same cardinality? - CORRECT ANSWER-
Cardinality is the term used to describe two infinite sets of objects that have the same
"number" of objects. Two sets have the same cardinality when there is a one-to-one
correspondence.
, What is a one-to-one correspondence? Explain how the sizes of two finite sets can be
compared without counting. Give an example. - CORRECT ANSWER- A one-to-one
correspondence when there is the same number of two objects. This can be used to compare
the size of two finite sets by pairing each object with another object from the other set.
Is there a one-to-one correspondence between UT students and UT EID's? Explain why or why
not. - CORRECT ANSWER- There is a one-to-one correspondence because each student has a
UT EID. Unless faculty have a UT EID then there would be more UT EIDs than there are
students.
Define or describe the following sets of numbers: natural numbers, integers, rational numbers,
real numbers. - CORRECT ANSWER- Natural: the positive intergers 1, 2, 3, 4, ...
Inegers: a whole number (not a fraction), can be either positive or negative.
Rational: any number that can be expressed as a fraction.
Real: any number that exists on the number line.
Do the natural numbers and the even numbers have the same cardinality? Explain. - CORRECT
ANSWER- Natural numbers and even numbers have the same cardinality because for every
natural number you can multiply it by two.
Do the natural numbers and the integers have the same cardinality? Explain. - CORRECT
ANSWER- Natural numbers and integers have the same cardinality. 0, -1, 1, -2, 2, -3, 3 (imagine
the snaking around)
Do the natural numbers and the rational numbers have the same cardinality? Explain. -
CORRECT ANSWER- Yes. Thread a rectangle around the two sets that are seperated by a 0.
They should be two squares that look like a pinwheel seperated by the 0.
QUESTIONS AND CORRECT DETAILED ANSWERS
(VERIFIED ANSWERS) |ALREADY GRADED A+||BRAND
NEW VERSION!!
Suppose a UT alum tells you their license plate is H00K3M. If you had a listing of all the
registered vehicles in the United States, would you be able to identify the vehicle belonging to
that person? Explain why or why not, using the idea of a one-to-one correspondence. -
CORRECT ANSWER- You would be able to identify the vehicle because there is a one-to-one
correspondence between licence plates and cars.
A professor wishes to distribute one exam paper to each student in the class. What is the more
efficient method: count students, or pass out exams? How does this relate to one-to-one
correspondence? - CORRECT ANSWER- The most efficient method is to pass out exams. Each
student present will receive one exam. This is the one-to-one crrespondence
Are there an infinite number of grains of sand on the Earth? Explain. - CORRECT ANSWER-
There is a finite number of grains of sand on Earth. It would be tedious but one could count or
estimate the number of grains of sand.
Define the term cardinality. When do two sets have the same cardinality? - CORRECT ANSWER-
Cardinality is the term used to describe two infinite sets of objects that have the same
"number" of objects. Two sets have the same cardinality when there is a one-to-one
correspondence.
, What is a one-to-one correspondence? Explain how the sizes of two finite sets can be
compared without counting. Give an example. - CORRECT ANSWER- A one-to-one
correspondence when there is the same number of two objects. This can be used to compare
the size of two finite sets by pairing each object with another object from the other set.
Is there a one-to-one correspondence between UT students and UT EID's? Explain why or why
not. - CORRECT ANSWER- There is a one-to-one correspondence because each student has a
UT EID. Unless faculty have a UT EID then there would be more UT EIDs than there are
students.
Define or describe the following sets of numbers: natural numbers, integers, rational numbers,
real numbers. - CORRECT ANSWER- Natural: the positive intergers 1, 2, 3, 4, ...
Inegers: a whole number (not a fraction), can be either positive or negative.
Rational: any number that can be expressed as a fraction.
Real: any number that exists on the number line.
Do the natural numbers and the even numbers have the same cardinality? Explain. - CORRECT
ANSWER- Natural numbers and even numbers have the same cardinality because for every
natural number you can multiply it by two.
Do the natural numbers and the integers have the same cardinality? Explain. - CORRECT
ANSWER- Natural numbers and integers have the same cardinality. 0, -1, 1, -2, 2, -3, 3 (imagine
the snaking around)
Do the natural numbers and the rational numbers have the same cardinality? Explain. -
CORRECT ANSWER- Yes. Thread a rectangle around the two sets that are seperated by a 0.
They should be two squares that look like a pinwheel seperated by the 0.
