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