show all work
w =Whol nambaer
Q=relation nambar
R=real nambar
W=1 2 3 4 5...
Q=p/q
{1 2 3 4 5}U{1/2 1/3 1/4 1/5 1/6 1/7....}
={+-1 +-2 +- 3 +-4 +-5 +-6.....}
So that WUQ=R
show all work w =Whol nambaer Q=relation nambar R=real nambar Prove thuit
Prove that the following relation R is an equivalence
relation on the set of ordered pairs of real numbers. Describe the
equivalence classes of R. (x, y)R(w, z)
y-x2 = z-w2
Discrete Math. Show all steps clearly
Define a relation R on the set of all integers Z as follows: Is R a partial order relation? Prove or give a counterexample.
Suppose R is the relation defined on all real numbers by for all real numbers x,y (xRy if |x-yl3) Then for real numbers x and y, xR2y iff
9. Let x,y > 0 be real numbers and q, r E Q. Prove the following: (а) 29 > 0. 2"а" and (29)" (b) x7+r (с) г а — 1/29. 0, then x> y if and only if r4 > y (d) If q (e) For 1, r4 > x" if and only if q > r. For x < 1, x4 > x* if and only if q < r.
Show all necessary work. Print your answers clearly 20 Show that the relation Ron ROR: the set of real numbers) given by Ry ill an equivalence relation. av
Prove that if R is an equivalence relation on a set A, then R ^-1 is an equivalence relation on A.
please show all your work clearly
Expert Q&A Done mu 3 R utath eomne on 0 Please show all your work
Expert Q&A Done mu 3 R utath eomne on 0 Please show all your work
Please do problem 9 and write a detailed proof when doing
(a)
9. Letbe the relation on the set of non-zero real numbers defined as follows: for r, y E R [0), x~ylf and only if-EQ (a) Prove thatis an equivalence relation. (b) Determine the equivalence class of π.
9. Letbe the relation on the set of non-zero real numbers defined as follows: for r, y E R [0), x~ylf and only if-EQ (a) Prove thatis an equivalence relation. (b)...
Let R be a relation on a set A. Prove that R is antisymmetric if and only if R ∩ R ^(−1) ⊆ {(a, a) : a ∈ A}.
8. Suppose that r" and q” are both solutions to a recurrence relation of the form an = aan-1+ Ban-2. Prove that c.pn + d.g” is also a solution to the recurrence relation, for any constants c, d.