1. I

    Understanding an Equivalence Relation proof

    Hey guys, I asked this question before but now I got the answer from my prof, but I don't really get the answer. A binary relation R is defined on the set Z2 as follows: (a, b) R (c, d) <---> a= c (mod 2) and b = d (mod 3) Here's what I don't get: From the definition, isn't reflexive (x, x)...
  2. I

    Prove an Equivalence Relation

    Hey, I would like to prove this equivalence relation: A binary relation R is defined on the set Z2 as follows: (a, b) R (c, d) <---> a= c and b = d I know I need to show that R is reflexive, symmetric, and transitive, but I am not sure how in this kind of question.
  3. M

    Symmetric Polynomials Involving Discriminant Polynomial

    Question: Let τ = (i, j) ∈ Sn with 1 ≤ i < j ≤ n. Prove: δ(rτ(1) , . . . ,rτ(n) ) = −δ(r1, . . . ,rn) Note: Discriminant Polynomial δ(r1,r2,.....,rn) = ∏ (ri - rj) for i<j I am pretty confused on where to begin. Based on the note, does −δ(r1, . . . ,rn) then =...
  4. D

    Proof : Let M be a symmetric positive stochastic matrix. Show that M + I is positive

    Can someone please help me with this exam question? Let M be a symmetric positive stochasticmatrix. Show that M + I is positive definite.
  5. U

    reflexive symmetric and transitive

    Hi, heres the question above and my go below: check reflexive: since the difference between similar birthdates is always less than one week, therefore xRx. Thus R is reflexive check symmetric: since the difference between birthdates is commutative then yRx. Thus R is symmetric. Please tell me...
  6. E

    L_n(V,F) is a subgroup of Sv, the symmetric group of V.

    Hi: In Group Theory, a book in the Schaum series, p.89, it says: "First let us define L_n(V,F) to consist of all one-to-one linear transformations of V, the vector space of dimension n over F. L_n(V,F) is included in Sv, the symmetric group of V, clearly". Then he uses this fact to prove that...
  7. S

    Help with binary relations (reflexive, symmetric, transitive...)

    I do not know where to start with the following question. Could someone please help me? Whenever I read examples in the book they make sense, but whenever I'm asked to do them I draw a blank. The furthest I got was proving reflexivity with the a). I said that x + 2x / 3 = x, but I don't...
  8. Jason76

    Parametric and Symmetric Equation

    Where did the x - 1, y + 1, and z -1 come from in the line below the underlined phrase "Parametric Equations"? Where did the equation v (arrow above it) = <1,2,1> come from?
  9. W

    Rn space symmetric?

    Hi! I came across with symmetric space definition that I haven't seen before, respectively, normed linear space X is symmetric if ||\lambda x-y||=||x-\lambda y||. It was mentioned that R^n space is clearly symmetric, but that does not seems true if we take Euclidean norm... How do you think?
  10. Y

    Symmetric bilinear form

    I am sort of lost in the following problem: Describe explicitly all symmetric bilinear forms on R^3 I would like to know how to approach this problem, because there is a one to one correlation with the quadratic form, but I am not sure if I should be using this.
  11. MechanicalPencil

    Subset of symmetric matricies proof

    Prove that the subset of symmetric (A^T=A ) matrices in Mnxn​ is a subspace. I know the 3 conditions of a subspace, I'm just trying to apply them in a way that satisfies the proof. Am I on the right track? Any help would be appreciated.
  12. R

    what is the symmetric closure of below relations?

    If I have a relation ,say ,less than or equal to ,then how is the symmetric closure of this relation be a universal relation . I tried out with example ,so obviously I would be getting pairs of the form (a,a) but how do they correspond to a universal relation.
  13. A

    Is the graph of "y = x^3/8" symmetric about the origin?

    Please explain why or why not!
  14. H

    Transitive subgroup of the symmetric group Sn

    Hi, I need help in proving the following statement: An abelian,transitive subgroup of the symmetric group Sn is cyclic,generated by an n-cycle. Thank's in advance
  15. M

    DISCRETE MATHEMATICS Reflexive Symmetric Transitive & Elements

    I'm new to the forum and look forward to be contributing. Thanks in advance guys. Let A = R x R the set of all ordered pairs (x,y), where x and y are real numbers. Define relation L on A as follows: For all (x,y) and (z,w) in A, (x,y) L (z,w) iff x - y = z - w. Prove that L is a) Reflexive...
  16. Wander

    Order of Elements in a Symmetric Group

    Hello! This question is stumbling me, and I feel like it should be completely trivial. (Worried) "Let G=Sym(6) be a symmetric group of 6 letters. How many elements in G have order 5?" My first thought was to try playing with Lagrange's theorem, which told me only that the order of an element...
  17. J

    find a basis for all symmetric M_3,3

    find a basis for all symmetric $M_{3,3}$ I am thinking$\Bigg\{$ $\begin{array}{cc}1&0&0\\0&0&0\\0&0&0\end{array} ,\begin{array}{cc}0&1&0\\1&0&0\\0&0&0\end{array},\\begin{array}{cc}0&0&1\\0&0&0\\1&0&0\end{array}$...
  18. C

    Symmetric with respect

    103. Show that a graph that is symmetric with respect to the x-axis and y-axis must be symmetric with respect to the origin. Give an example to show that the converse is not true. I understand I have to display a graph that is symmetric with respect to the x-axis and y-axis must be symmetric...
  19. M

    reflexive, not symmetric but transitive

    let A={a,b,c} and B ={2,3,4} and R= {(a,1),(c,3),(b,4),(b,2)} Give a relation on A that is reflexive, not symmetric but transitive. show that the relation has the desired properties. How do i go about doing this? thanks
  20. C

    Reflexive, Symmetric, Transitive Relation Proof

    Let X be a set and let R be the relation "" defined on subsets of X. Prove whether reflexive, symmetric, transitive. Is this the right approach? Proof: (Reflexive) Suppose S is a subset of X. Suppose y is in S. (Now I need to show that (y, y) is in R. Can I say that y y, so (y, y) is in R...