D420 Discrete Math: Functions and Relations - Set 1 - Part 3

Test your knowledge of technical writing concepts with these practice questions. Each question includes detailed explanations to help you understand the correct answers.

Question 41: Which of the following best describes the principle of strong mathematical induction?

The statement must be proven true for all values of n at once

The statement must be true for the base case and hold for all k before proving it for k+1

The statement must be true for k+1 in order to prove it for all values of k

The statement must be true for even numbers to be true for odd numbers

Question 42: Which of the following is true for an r-permutation of a set?

It is an unordered selection of r elements from the set

It is an ordered arrangement of r elements from the set

It is an unordered arrangement of all elements from the set

It is an ordered arrangement of all elements from the set

Question 43: What is the difference between a permutation and a combination?

A permutation involves order, while a combination does not

A combination involves order, while a permutation does not

Both permutations and combinations involve order

Neither permutations nor combinations involve order

Question 44: What does the inclusion-exclusion principle calculate?

The number of elements in the union of two or more sets

The number of elements in the intersection of two or more sets

The number of elements in a Cartesian product

The number of elements in the complement of a set

Question 45: Which of the following statements is true for a binary relation on set A?

It relates elements of set A to elements of set B

It relates elements of set A to themselves

It relates every element of set A to every other element of set A

It relates elements of set A to elements of set A

Question 46: Which of the following describes a reflexive relation?

If a is related to b, then b is related to a

Every element in the set is related to itself

No element is related to any other element

Every element is related to every other element

Question 47: Which of the following describes a symmetric relation?

If a is related to b, then b must also be related to a

If a is related to b, then a must be greater than b

If a is related to b, then a must be equal to b

If a is related to b, then a must not be related to b

Question 48: Which of the following is true for a transitive relation?

If a is related to b and b is related to c, then a must be related to c

If a is related to b, then b must also be related to a

If a is related to b, then a must not be related to b

If a is related to b, then a must be equal to b

Question 49: What is a strict order?

A relation that is transitive and anti-reflexive

A relation that is reflexive and symmetric

A relation that is transitive and symmetric

A relation that is reflexive and transitive

Question 50: What is a directed acyclic graph (DAG)?

A directed graph with no positive length cycles

A graph where every vertex is connected to every other vertex

A graph where all edges are undirected

A graph with exactly one cycle

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