Intro to college math Exam Questions
and Answers
Define an irrational number in two ways - correct answer-1. Non- terminating
2. Can't be written as a fraction
Find a rational number and an irrational number that is bigger than 12.05691 but smaller
12.05692. - correct answer-↔ 12.056920
12.056910
rat- 12.056915
irrat- 12.0569151151115115.....
Express the following rational numbers as fraction. - correct answer-a) 20.4545:
b) 20.454545:
c) 3.10232323..:
Is it possible to build an irrational number whose decimal digits are 1's and 2's? If so,
describe such a number and show why it's irrational. If not, explain why. - correct
answer-Yes, .121121112....
.12112111211112..... (rational)
Which statement is true?
(I) Every set of Natural numbers contains a smallest number.
(II) Every set of Natural numbers contains a biggest number. - correct answer-(I) Yes, 1
(II) No, infinity
Use a proof by contradiction to prove that there is no greatest even number. - correct
answer-Assume N is the greatest even #:
2n+2/2 ↔ add to 2 to n
, Prove that the product of 2 irrational numbers can be rational. (Proof by counter
example) - correct answer-a/b x c/d= ac/bd
Prove that 1/√2is irrational. - correct answer-Assume it's rational ↔ 1/2= a/b
a√2=b √2=a/b
I=R
Give an example to show the sum of two irrational numbers can be rational. - correct
answer-√2 + √-2= 0
0 is a rational # !
What does it mean for two sets to have the same cardinality? - correct answer-They had
a 1-1 correspondence
Every child has one and only one birth mother. Does that imply that there is 1-1
correspondence between the set of all birth mothers and children? - correct answer-NO,
because a mother can have more than 1 child.
Show by way of an example that there are subsets of N having the same cardinality as
N. - correct answer-12345
⇅ 1-1 correspondence
23456
This can't happen with finite sets.
Natural Numbers
Integers
Rational Numbers - correct answer-1,2,3... (whole #s)
Negative and whole #s
Fractions
Proper Fraction
Reduced Fraction
The reciprocal of a number x. - correct answer-Numerator is smaller than the
denominator
Any fraction with no common divisors
and Answers
Define an irrational number in two ways - correct answer-1. Non- terminating
2. Can't be written as a fraction
Find a rational number and an irrational number that is bigger than 12.05691 but smaller
12.05692. - correct answer-↔ 12.056920
12.056910
rat- 12.056915
irrat- 12.0569151151115115.....
Express the following rational numbers as fraction. - correct answer-a) 20.4545:
b) 20.454545:
c) 3.10232323..:
Is it possible to build an irrational number whose decimal digits are 1's and 2's? If so,
describe such a number and show why it's irrational. If not, explain why. - correct
answer-Yes, .121121112....
.12112111211112..... (rational)
Which statement is true?
(I) Every set of Natural numbers contains a smallest number.
(II) Every set of Natural numbers contains a biggest number. - correct answer-(I) Yes, 1
(II) No, infinity
Use a proof by contradiction to prove that there is no greatest even number. - correct
answer-Assume N is the greatest even #:
2n+2/2 ↔ add to 2 to n
, Prove that the product of 2 irrational numbers can be rational. (Proof by counter
example) - correct answer-a/b x c/d= ac/bd
Prove that 1/√2is irrational. - correct answer-Assume it's rational ↔ 1/2= a/b
a√2=b √2=a/b
I=R
Give an example to show the sum of two irrational numbers can be rational. - correct
answer-√2 + √-2= 0
0 is a rational # !
What does it mean for two sets to have the same cardinality? - correct answer-They had
a 1-1 correspondence
Every child has one and only one birth mother. Does that imply that there is 1-1
correspondence between the set of all birth mothers and children? - correct answer-NO,
because a mother can have more than 1 child.
Show by way of an example that there are subsets of N having the same cardinality as
N. - correct answer-12345
⇅ 1-1 correspondence
23456
This can't happen with finite sets.
Natural Numbers
Integers
Rational Numbers - correct answer-1,2,3... (whole #s)
Negative and whole #s
Fractions
Proper Fraction
Reduced Fraction
The reciprocal of a number x. - correct answer-Numerator is smaller than the
denominator
Any fraction with no common divisors
