First, let’s take a look at the relevant definitions that we need to know to solve this exercise. Definition: “A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.” Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element […]
Below are the relevant definitions that we need to know to solve this exercise. Definition: “A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.” Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element a ∈ A.” Definition:
Let’s start with the relevant definitions that will help us to solve this exercise. Definition: “A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.” Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element a ∈ A.” Definition:
As usual for us, we will start refreshing the relevant definitions to solve this exercise. Definition: “A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.” Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element a ∈ A.”
Let’s refresh the relevant definitions for this exercise. Definition: “A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.” Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element a ∈ A.” Definition: “A relation R on a set
As usual, let’s start with the definitions. Definition: “The compound propositions p and q are called logically equivalent if p ↔ q is a tautology. The notation p ≡ q denotes that p and q are logically equivalent.” Notice that if p ↔q is a tautology, p and q have the same truth values. Definition:
I found out that some students want to solve this type of exercise, where they need to answer if a relation is an equivalence relation, but they don’t know what an equivalence relation is. By doing this, you have a high probability of answering wrong. So, let’s start with the definitions. Definition: “A relation on
a) {(a,b)|a>b}? To answer this exercise, let’s find out how many 1s will have in each row. Then, we add them up. The last row (row 100) will have ninety-nine 1s because 99 numbers are less than 100 in the set A={1,2,3,…,100}. The second last row (row 99) will have ninety-eight 1s as 98 numbers
This is an interesting type of exercise. To make easier this exercise, let’s write an irreflexive relation, represent it using a matrix, and find out what are the characteristics of such a matrix. But first, let’s refresh what an irreflexive relation is. Definition: “A relation R on the set A is irreflexive if for every
In this case, we are given the matrix that represents the relation, and we need to write the pairs that belong to the relation. It is the opposite of this exercise. a) Matrix 1 The approach to solving this type of exercise is to find where there is a 1 in the matrix and write
