I am a bit confused whether the following relation is an equivalence relation or not. $\sim$ is defined on the set of all integers $x \sim y$ if and only if $x = \pm y$. I thought this is an equivalence relation since I checked it for reflexivity, symmetry, and transitivity and according to my scratch work, all of them are satisfied. Am I missing something or am I on the right track?
2026-04-11 21:33:09.1775943189
Checking whether a relation is an equivalence relation
36 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DISCRETE-MATHEMATICS
- What is (mathematically) minimal computer architecture to run any software
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Given a function, prove that it's injective
- Surjective function proof
- How to find image of a function
- Find the truth value of... empty set?
- Solving discrete recursion equations with min in the equation
- Determine the marginal distributions of $(T_1, T_2)$
Related Questions in SOLUTION-VERIFICATION
- Linear transform of jointly distributed exponential random variables, how to identify domain?
- Exercise 7.19 from Papa Rudin: Gathering solutions
- Proof verification: $\forall n \in \mathbb{Z}, 4\nmid(n^2+2)$
- Proof verification: a function with finitely many points of discontinuity is Riemann integrable
- Do Monoid Homomorphisms preserve the identity?
- Cantor-Lebesgue's theorem
- If $a$ is an integer, prove that $\gcd(14a + 3, 21a + 4) = 1$.
- Number theory gcd
- $|G| > 1$ and not prime implies existence of a subgroup other than two trivial subgroups
- Prove/Disprove: Sum of im/ker of linear transformation contained in ker/im of each linear trasnfromation
Related Questions in RELATIONS
- How are these definitions of continuous relations equivalent?
- Is a relation on which every element is related with itself alone transitive?
- Relation power composition
- Order relation proof
- Order relation proof ...
- How to identify if a given Hasse diagram is a lattice
- Is the relation < a strict total order?
- Is there a name for this property on a binary relation?
- Finding all reflexive binary relations of a set
- Showing that a relation is reflexive, symmetric and transitive
Related Questions in EQUIVALENCE-RELATIONS
- Relations of equivalence...
- Number of subsets, relations etc of a set
- Number of possible equivalence relations
- Why is $p(z) = \frac{e^z}{1 + e^z} \color{red}{\equiv} \frac{1}{1 + e^{-z}}$ and not $=$?
- Simple question about relations
- Total number of equivalence class for a set
- Is this an equivalence relation and explaination?
- Partition of a set identified by a equivalence relation
- Define an equivalence relation on $\{ 1,2,3,4 \}^2$ by: (, )(, ) if ⋅ = ⋅ . How many equivalence classes are there?
- Prove that $\sum_{i=1}^n\lvert[a_i]\rvert$ is even iff $n$ is even
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?