MATH 230 QUESTIONS AND ANSWERS WITH SOLUTIONS 2024

MATH 230 QUESTIONS AND ANSWERS
WITH 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