Exam (elaborations)
MATH 230 QUESTIONS AND ANSWERS WITH SOLUTIONS 2024
- Course
- Institution
MATH 230 QUESTIONS AND ANSWERS WITH SOLUTIONS 2024
[Show more]
Content preview
MATH 230 QUESTIONS AND ANSWERSWITH SOLUTIONS 2024
Which is the best 'definition' of the term 'definition' in mathematics? - ANSWER A statement of the exact
meaning of a concept or precise description of an object
Which is a false statement about axioms in mathematics? - ANSWER We do not need to state the axioms
to use them
Which is a true statement in logic? - ANSWER There are statements that are always true
Which operations on numbers are well defined in the set of natural numbers N? - ANSWER Addition and
multiplication only
Which operations on numbers are well defined in the set of integers Z? - ANSWER Addition, subtraction
and multiplication only
Which operations on numbers are well defined in the set of rational numbers Q? - ANSWER Addition,
subtraction, multiplication and division (except by 0) only
Which operations on numbers are well defined in the set of real numbers R? - ANSWER Addition,
subtraction, multiplication, division (except by 0) and taking radicals and limits
Which operations are well defined in the set of complex numbers C? - ANSWER Addition, subtraction,
multiplication, division (except by 0) and solving algebraic equations
Mark all sets that have the set of rational numbers Q as a proper subset. - ANSWER The set of complex C
and the set of real numbers R
Mark the sets that are NOT contained in the set of real numbers R as a proper subset. - ANSWER The set
of imaginary numbers
For any two sets ( C u B)' = - ANSWER C' n B'
,Which of the following are valid for any sets F and G:
1) F - G = G - F
2) F' = G
3) F u G = G' u F'
4) F u G = G u F
5) F n G = G n F
6) F n G - F = G - G - ANSWER Last 3 are valid
Let Z be the universe for the following two sets A = { x > 4} and B = { 2 < x < 10}. What is (A n B)' = ? -
ANSWER (A n B)' = {. . . -1, 0, 1, 2, 3, 4, 10, 11. . . )
A is a subset of B. Which of the following is NOT true? - ANSWER B - A = empty set
Consider R to be the universe for the following sets.
N = (1,2,3,4 .... ) Z= {...-3, -2, -1, 0, 1, 2 , 3 ....} Even = ( ...-4, -2, 0, 2 , 4 ...} R+ = {all positive decimals}
Note : u - means 'union'; n means 'intersection' , A' - means a complement to A
Check all statements below that are true. - ANSWER N u R+ = R+
Z - Even = Odd
Z u Even = Z
(R+ )' = {all non positive reals}
(Z n N )'= {all reals that are not natural numbers}
R+ - Z = {all positive real numbers that are not integer}
U = {all students in our logic class}.
Let A = { math majors}, B = {current calculus students}, C= {students who play an instrument }
C n A' n B = - ANSWER { non math majors who take calculus students and play an instrument }
U = {all people in USA} . Let A = {all university students}, B = {people in California}.
, Then (A u B)' = - ANSWER {Non Californians who are not students}
R (the set of reals) is the universe . A= (1,4 ) B= [-3, 2] R+ = {all positive decimals} .
Check all true statements below. - ANSWER R+ - B = (2, infinity)
R+ u (R+ )' = R
A n B = (1, 2]
A - R+ = Empty set
A u B = [-3, 4)
A = {a, b, c}. Check the true statement about the power set of A (called 2 A ) - ANSWER 2 A has
cardinality 8
N = {natural numbers}. Check all correct statements about the power set 2N . - ANSWER {0} is an
element of 2N
2N contains the set of natural numbers N as an element
2N contains empty set as an element
{1}, {1 ,2}, {1,2,3} , {1,2,3,4} are some of the elements of 2N
2N is infinite
{even natural numbers} are an element of 2N
When two infinite sets are equal? - ANSWER If all their elements are the same
When two infinite sets have the same cardinality? - ANSWER When there is 1:1 correspondence
between their elements
Let F = {all positive fractions smaller than 1}. Which of the following statements is not true :
F is a subset of Q
We can number the elements of F 1,2,3,4 ...
We can make a list of the elements of F
F has as many elements as Q
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Performance. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $17.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75391 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now