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WorksheetsQuiz 1-3_Abstract
Total questions: 45
Worksheet time: 2hrs 30mins
In modular arithmetic, is it always true that (a + b) mod m = (a mod m) + (b mod m)?
No, it depends on the values of a, b, and m
Yes, this is always true
Only if a and b are relatively prime to m
Only if m is a prime number
Find (8 * 3) mod 7.
1
3
24
56
If 2x ≡ 8 (mod 6), what is the solution for x?
2
3
4
5
Find the modular multiplicative inverse of 2 modulo 11.
There is no inverse
1
2
6
What is the remainder when 17 is divided by 4?
1
2
3
4
Solve the congruence: x ≡ 17 (mod 12).
5
17
29
There is no solution
If a ≡ b (mod m) and c ≡ d (mod m), is it always true that (a + c) ≡ (b + d) (mod m)?
No, it depends on the values of a, b, c, d, and m
Yes, this is always true.
Only if a and c are relatively prime to m
Only if b and d are relatively prime to m
For a given set of triangles, the relation of 'is similar to ()' and 'is congruent to ()' not shows equivalence.
True
False
Modular arithmetic is useful in various applications. Which of the following is NOT a common use case?
Error detection in data transmission
Public-key cryptography
Clock arithmetic (e.g., 12-hour clock)
Direct calculation of square roots
He is a German Mathematician who gave the modern definition of function in 1837.
Peter Derichlet
Peter Direchlet
Peter Dirichlet
Peter Derechlet
Is a function in which each input value is mapped to one unique output value.
Inverse Function
One-to-One Function
One-to-One Correspondence
Onto One Function
If a ≡ b (mod m), what does this notation mean?
a is less than b by m
a is a multiple of b and m
a and b have the same remainder when divided by m
a is greater than b by m
What property allows us to add and subtract congruence's with the same modulo?
Commutative property
Congruence rule
Associative property
Distributive property
One-to-One Correspondence is also called __________?
Bijective
Surjective
Injective
One-to-One Function
What does "7 mod 3" represent?
The difference between 7 and 3
The product of 7 and 3
The remainder when 7 is divided by 3
The quotient when 7 is divided by 3
Modular arithmetic is useful in which of the following applications?
Clock arithmetic (e.g., 12 hours on a clock)
Standard unit conversions (e.g., meters to centimeters)
Traditional long division
None of the above
What is NOT true about modular arithmetic?
Addition and multiplication can be performed.
The modulo (m) is always a positive integer.
Negative numbers can be used directly in calculations.
The result of a modular operation is always less than the modulo.
This relationship is commonly symbolized as y = f(x) which is said "f of x" and y and x are related such that for every x, there is a unique value of y.
Range
Notation
Function
Domain
Who introduced the term surjective function?
Nicolas Bourbaki
Peter Dirichlet
Nicholas Bourbaki
Peter Derichlet
It is a system of arithmetic for integers, where numbers "wrap around" after reaching a certain value, which is often referred to as the modulus
Analytic Geometry
Modulus Arithmetic
Modular Inverse
Modulus Operator
In modular arithmetic, what is the most important concept?
The base number
The modulo
The result
The operation
It is a function which can reverse into another function
Inverse Function
One-to-One Function
One-to-One Correspondence
Onto One Function
If for every element of B, there is at least one or more than one element matching with A, then the function is said to be ____________.
Inverse Function
One-to-One Function
One-to-One Correspondence
Onto one function
The inverse function is also called the reciprocal function. This statement is _______.
True
False
Maybe
I don't know
Find the inverse of the function f(x) = 2x + 3A.
f(−1)(x)=2x−3
f(−1)(x)=3(x-2)
f(−1)(x)=2(x-3)
f(−1)(x)=3(x+2)
(1,2),(3,4),(5,6),(7,8) What is the domain of the given data set?
(1, 2, 3, 4)
(1, 3, 5, 7)
(2, 4, 6, 8)
This is not a function
It is all the function's outputs, dependent variables, or y-values
Range
Domain
Relation
Function
It is all the inputs accepted by the function
Range
Domain
Relation
Function
A function is a relation that maps each element x of a set A with one and only one element y of another set B
The statement is correct.
The statement is wrong.
None of the above
An ordered pair of elements “a” to “b” (aRb) and “b” to “c” (bRc) is present in relation R, then an ordered pair of elements “a” to “c” (aRc) should also be present in the relation R
Equivalence relation
Transitive
Symmetric
A binary relation defined on a set X such that the relation is reflexive, symmetric, and transitive. If any of the three conditions (reflexive, symmetric, and transitive) does not hold, the relation cannot be ______________.
Equivalent
Equivalence relation
Elements
Equivalence relations are often used to group together objects that are similar, or “________”, in some sense
Equivalent
Equivalence relation
Elements
An ordered pair of elements “a” to “b” (aRb)is present in relation R, then an ordered pair of elements “b” to “a” (bRa) should also be present in relation R
Symmetric
Reflexive
Transitive
Element “a” is present in set A, then a relation “a” to “a” (aRa) should be present in relation R
Transitive
Symmetric
Reflexive
An equivalence relation is a binary relation defined on a set X such that the relation is inverse, symmetric, and transitive
True
False
The equivalence relation is a relationship on the set which is generally represented by the symbol “”
True
False
Element “a” is present in set A, then a relation “a” to “a” (aRa) should be present in relation R. If any such aRa is present in R then R is not a reflexive relation
True
False
For a given set of integers, the relation of ‘congruence modulo n ()’ shows the relation of equivalence
True
False
What is the result of (15 + 8) mod 5?
2
3
4
5
Define the term "congruence modulo n" in modular arithmetic.
It represents the difference between two numbers.
It signifies that two numbers have the same remainder when divided by n.
It indicates that two numbers are prime to each other.
It denotes the product of two numbers.
What is the modular multiplicative inverse of 5 modulo 12?
1
2
5
11
What is the main application of modular arithmetic in error detection?
Checksum calculation
Sorting algorithms
Graph theory
Database management
When is the concept of modular arithmetic most commonly used in cryptography?
Key generation
Data compression
Image processing
Network routing
How does modular arithmetic help in simplifying calculations involving large numbers?
By reducing the number of operations needed
By increasing the precision of the results
By eliminating the need for division
By converting numbers to binary form
BONUS Question.
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